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Wireless Communications and Control for Swarms
of Cellular-Connected UAVs
Tengchan Zeng1, Mohammad Mozaffari2, Omid Semiari3, Walid Saad1, Mehdi Bennis4, and Merouane Debbah5
1Wireless@VT, Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA, USA,
Emails:{tengchan, walids}@vt.edu.
2Ericsson, Santa Clara, CA, USA, Email: mohammad.mozaffari@ericsson.com.
3Department of Electrical and Computer Engineering, Georgia Southern University, Statesboro, GA, USA,
Email: osemiari@georgiasouthern.edu.
4Centre for Wireless Communications, University of Oulu, Oulu, Finland, Email: mehdi.bennis@oulu.fi.
5Mathematical and Algorithmic Sciences Lab, Huawei France R&D, Paris, France, Email: merouane.debbah@huawei.com.
Abstract—By using wireless connectivity through cellular base
stations (BSs), swarms of unmanned aerial vehicles (UAVs) can
provide a plethora of services ranging from delivery of goods
to surveillance. In particular, UAVs in a swarm can utilize
wireless communications to collect information, like velocity and
heading angle, from surrounding UAVs for coordinating their
operations and maintaining target speed and intra-UAV distance.
However, due to the uncertainty of the wireless channel, wireless
communications among UAVs will experience a transmission
delay which can impair the swarm’s ability to stabilize system
operation. In this paper, the problem of joint communication
and control is studied for a swarm of three cellular-connected
UAVs positioned in a triangle formation. In particular, a novel
approach is proposed for optimizing the swarm’s operation while
jointly considering the delay of the wireless network and the
stability of the control system. Based on this approach, the
maximum allowable delay required to prevent the instability of
the swarm is determined. Moreover, by using stochastic geometry,
the reliability of the wireless network is derived as the probability
of meeting the stability requirement of the control system. The
simulation results validate the effectiveness of the proposed joint
strategy, and help obtain insightful design guidelines on how to
form a stable swarm of UAVs.
I. INTRODUCTION
The deployment of unmanned aerial vehicles (UAVs), pop-
ularly known as drones, is rapidly increasing and will lead to
the introduction of numerous application services ranging from
delivery of goods to surveillance and smart city monitoring [1].
In particular, driven by the ever-decreasing cost of manufacture
components and the emergence of new services, the use of
UAV swarms is rapidly gaining popularity [2]–[7].
In addition, by using swarms of UAVs, one can complete
more sophisticated missions in an uncertain and possibly
hostile environment. For example, swarms of drones have
been used for Amazon’s prime air drone delivery services and
emergency medicine delivery services [2]. Also, in [4], groups
of UAVs have been used to create a reconfigurable antenna
array in the sky so as to provide wireless service to ground
users. Moreover, swarms of micro drones are being actively
investigated by DAPRA’s VisiBuilding program to complete
reconnaissance missions inside buildings [5]. Furthermore, the
authors in [6] and [7] proposed to deploy multiple UAVs,
which function as wireless base stations (BSs) or relays, so
as to maximize the wireless coverage.
This research was supported by the U.S. National Science Foundation under
Grant CNS-1739642.
In particular, to complete their assigned missions, the UAVs
in the swarm will have to communicate with BSs via cellular
links for various purposes such as sending collected surveil-
lance and monitoring information back to the BSs. Moreover,
to guarantee a safe operation and avoid collisions between
UAVs within the swarm, the UAVs will use the information
received from the intra-swarm wireless network as an input
of the control system. That is, each UAV can first use intra-
swarm communications to obtain information of other UAVs
in the swarm, such as their velocity and heading angle. Then,
the control system of each UAV will use sensor data and
the information received from the wireless links to coordinate
UAV’s movements. However, due to the uncertainty of the
wireless channel and the presence of wireless interference,
the received information from wireless links will inevitably
suffer from transmission delay, and the delayed information
can impair the ability of the control system to coordinate the
UAVs’ movements [8]. As a result, when designing a swarm
of UAVs, we need to jointly consider the control system and
wireless network to guarantee a stable formation.
The prior art working on wirelessly connected swarms
of UAVs can be grouped into two categories. In particular,
the first category focuses on the intra-swarm communication
network design [9] and [10]. For example, the authors in
[9] proposed a multicluster flying ad-hoc network to reduce
the power consumption while maintaining an acceptable level
of communication latency for UAV swarms. Furthermore, a
wireless mesh network is proposed in [10] to improve the
connectivity of a swarm of UAVs and build a pervasive
networking environment. However, prior works, such as [9]
and [10], ignore the impact of wireless system on the stability
of the UAV and solely focus on the communication system
design. The second category focuses on coordination and
control for effective task planning for UAVs [11] and [12].
For example, in [11], a heuristic multi-UAV task planning
algorithm is proposed to enable a swarm of cellular connected
UAVs to visit all target points in a minimum time. In addition,
the authors in [12] proposed a behavioral flocking algorithm
for distributed flight coordination of multiple UAVs. Note that,
such control-centric works, like [11] and [12], assume a fixed
wireless performance or just ignore the transmission delay
generated by communication links when designing the control
system. Such an assumption is certainly not practical for UAV
UAV 1
UAV 2
UAV 3
Leader
Follower
Follower
BS
Fig. 1. A swarm of three UAVs where each UAV can communicate with the
BS. UAV 1 is the leader, and UAVs 2 and 3 are followers.
swarms that use a cellular network due to the uncertainty
of wireless channels and interference generated by coexisting
wireless links.
The main contribution of this paper is a novel approach
to jointly design the control and communication system for a
cellular-connected swarm of UAVs. In particular, we first ana-
lyze the stability of the control system which can guarantee a
stable triangle formation for a swarm of three UAVs. Then, we
determine the maximum transmission delay that the considered
swarm can tolerate without jeopardizing its control system’s
stability. This threshold can, in turn, be used to identify the
reliability requirement for the wireless communication system.
In particular, we use stochastic geometry to mathematically
characterize the reliability of the wireless network. Simulation
results validate the effectiveness of the proposed integrated
communication and control strategy, and help obtain new
design guidelines on how to create a stable formation for
a swarm of UAVs. For example, our results provide clear
guideline on how to choose the target spacing for the swarm so
as to guarantee a target reliability performance for the wireless
network.
The rest of this paper is organized as follows. Section
II presents the system model. In Section III, we perform a
stability analysis for the control system for the swarm of UAVs
and derive the mathematical expression for the reliability of
the wireless network by using stochastic geometry. Section IV
provides the simulation results and conclusions are drawn in
Section V.
II. SY ST EM MO DE L
Consider a swarm of three UAVs flying at the same altitude.
In this swarm, two UAVs are following a third, leading UAV
to form and maintain a triangle formation, as shown in Fig.
1. In this model, we assume that UAV 1is the leading UAV
that always flies with a target velocity and heading direction,
while UAVs 2and 3are followers. Note that, when following
the leading UAV, UAVs 2and 3will also need to keep a
certain target distance with each other and with the leader. For
each UAV, an embedded radar sensor can sense the distance
to the nearby UAVs. Moreover, each following UAV can
communicate with the two other UAVs in the swarm, via
wireless cellular links, to obtain information of the velocity
and heading angle. In addition, each UAV will communicate
with the BSs through cellular links to report its movement
and location or to complete tasks, like sending the collected
surveillance information back to the BSs.
A. Control System Model
As shown in Fig. 1, we consider a Cartesian coordinate
system centered on an arbitrarily selected point, and the
location of each UAV at time tis denoted by (xi(t), yi(t)), i ∈
{1,2,3}. Also, by using the coordinate system, we can de-
compose the velocity of each UAV into two components: one
on the x-axis and the other one on the y-axis. Moreover, we
assume that the control laws of each following UAV over the
x-axis and y-axis depend on the difference between the actual
distance to the UAVs in the swarm and the target distance. For
example, if the actual distance between a following UAV and
other UAVs in the swarm exceeds the corresponding target
spacing, the following UAV needs to accelerate in order to
reduce the spacing and reach the target distance. To determine
the control law on each axis, we first take the component on
the x-axis as an example. In particular, we define the x-axis
distance difference by using the following spacing errors:
δx
1,2(t)=x1(t)−x2(t)−¯x1,2, δx
1,3(t)=x1(t)−x3(t)−¯x1,3,(1)
δx
2,3(t)=x2(t)−x3(t)−¯x2,3, δx
3,2(t)=x3(t)−x2(t)−¯x3,2,(2)
where ¯x1,2,¯x1,3,¯x2,3,and ¯x3,2are the target x-axis spacing
between the corresponding UAVs. Note that xi(t)−xj(t)is
usually considered as the x-axis headway distance between
UAVs iand jwith i, j ∈ {1,2,3}, at time t. Also, we can
define the x-axis velocity errors for following UAVs 2and 3
as
zx
2(t) = vx
2(t)−¯vx, zx
3(t) = vx
3(t)−¯vx,(3)
where ¯vxis the x-axis component of the target operating
velocity for the swarm of UAVs. Note that the spacing errors
and velocity errors on the y-axis can be derived as done in
(1)–(3) and are omitted due to space limitations.
Similar to the dynamical system model introduced in [13],
the acceleration and deceleration of each UAV will depend on
the spacing errors and velocity errors. In particular, the x-axis
control law for each following UAV can be given by:
ux
i(t)=aiδx
1,i +bi[vx
1(t−τ1,i(t))−vi(t)]+ ˆaiδx
j,i
+
ˆ
bi[vj(t−τj,i(t))−vi(t)], i 6=j, i, j ∈{2,3},(4)
where ai,bi,ˆai, and ˆ
biare the associated gains for each
corresponding term, while τj,i captures the delay for the
wireless link from UAV jto UAV i. Note that the associated
gains essentially capture the sensibility of the control system to
changes in distance and velocity. Also, since the leading UAV
always flies with the target velocity and heading angle, then
the solution to vx
1(t−τ1,i(t)) = ¯vxalways exists. Similarly,
we can also derive the control law over the y-axis for each
following UAV. Therefore, based on the x-axis and y-axis
control laws for the velocity components, we can determine
how the velocity and heading angle of each following UAV
should change.
B. Wireless Communication System
For the wireless communication links between UAVs inside
the swarm, we consider an orthogonal frequency-division
multiple access (OFDMA) scheme where each communication
link does not share the frequency resource with other links in
the swarm. In this case, the wireless links in the swarm can
coexist without suffering from interference from each other.
However, the wireless links in one swarm can experience
interference when other UAVs at the same altitude that are
using the same frequency resource to transmit information
with each other or with BSs via cellular links. To have a
general interference model, we assume that the distribution of
interfering UAVs at the same altitude with the swarm follows
a 2-dimensional Poisson point process (2-D PPP) with density
λ. Also, similar to [14], we consider the wireless communi-
cation channels inside the swarm as independent Nakagami
channels with parameter β, and we also model the wireless
channels from interfering UAVs to UAVs inside the swarm
as independent Rayleigh fading channels. Thus, the channel
gain between a receiving UAV iand a transmitter jat time
twill be gj,i(t) = hj,i (t)(dj,i(t))−α, where hj,i (t)captures
the fading gain, dj,i(t)is the distance between UAVs jand i,
and αis the path loss exponent. Moreover, we can obtain the
received signal at UAV ias Pj,i(t) = Ptgj,i(t), where Ptis
the transmission power. Also, the signal-to-interference-plus-
noise-ratio (SINR) can be given by γj,i(t) = Pj,i(t)
σ2+Ii(t), where
σ2is the variance of the Gaussian noise, and Ii(t)captures the
interference experienced by UAV i. Then, the data rate will
be: Rj,i(t) = ωlog2(1 + γj,i (t)), where ωis the bandwidth
of the frequency resource. Whenever all packets are of equal
size Sbits, the transmission delay of the wireless link between
UAVs jand ican be derived as
τj,i(t) = S
ωlog2(1 + γj,i(t)) .(5)
In the following section, we take into account the time-varying
wireless transmission delay in (5) and analyze its effect on the
stability of the control system in the swarm of UAVs.
III. STABI LI TY AN ALYS IS F OR T HE SWAR M OF UAVS
For the swarm of UAVs, the delayed information received
from the wireless links can negatively impact the control
system’s ability to coordinate the movements. As a result, the
target formation for the swarm of UAVs may fail to form.
Here, we perform a stability analysis for the swarm under the
influence of the transmission delay. In particular, we determine
the transmission delay threshold which can guarantee that the
following UAVs will fly at the same speed and heading angle
with the leading UAV and keep the target distance to the
other UAVs in the swarm. Based on the stability analysis, we
employ stochastic geometry to mathematically characterize the
reliability of the wireless system, defined as the probability
that the wireless system can meet the control system’s delay
requirements.
A. Stability Analysis
To guarantee that each following UAV operates at the same
speed and heading angle as the leading UAV and keeps a
target distance to UAVs in the swarm, both spacing errors
and velocity errors on the x-axis should converge to zero. To
this end, we take the first-order derivative of (1), (2), and (3)
as follows:
˙
δx
1,2(t) = −zx
2(t),˙
δx
1,3(t) = −zx
3(t),(6)
˙
δx
2,3(t) = −˙
δx
1,2(t) + ˙
δx
1,3(t),˙
δx
3,2(t) = ˙
δx
1,2(t)−˙
δx
1,3(t),(7)
˙zx
2(t) =(a2+ ˆa2)δx
1,2(t)+(−ˆa2)δx
1,3(t)+
(−b2−ˆ
b2)(zx
2(t)) + ˆ
b2zx
3(t−τ3,2(t)),(8)
˙zx
3(t) =(a3+ ˆa3)δx
1,3(t)+(−ˆa3)δx
1,2(t)+
(−b3−ˆ
b3)(zx
3(t)) + ˆ
b3zx
2(t−τ2,3(t)),(9)
where ˙
δx
1,2(t),˙
δx
1,3(t),˙
δx
2,3(t),˙
δx
3,2(t),˙zx
2(t), and ˙zx
3(t)are vari-
ables differentiated with respect to time t. Additionally, since
the channel gains of the wireless links between UAVs 2and
3and between UAVs 3and 2follow the same distribution,
we assume τ2,3(t) = τ3,2(t) = 4τ(t). After collecting the
spacing and velocity errors for all following UAVs, we can
find the augmented error state vector at the x-axis ex(t) =
[δx
1,2(t), δx
1,3(t), zx
2(t), zx
3(t)]Tand obtain
˙
ex(t) = M1ex(t) + M2ex(t− 4τ(t)),(10)
where
M1=
0 0 −1 0
0 0 0 −1
a2+ ˆa2−ˆa2−b2−ˆ
b20
−a3(a3+ ˆa3) 0 −b3−ˆ
b3
,(11)
and
M2=
0 0 0 0
0 0 0 0
0 0 0 ˆ
b2
0 0 ˆ
b30
.(12)
Since the stability of the swarm of UAVs requires the x-
axis spacing and velocity errors of all following UAVs to
approach zero, the error vector ex(t) = 04×1should be at
least asymptotically stable.
Guaranteeing the stability for a wireless-connected swarm
will hence require a small wireless transmission delay. There-
fore, next, as a direct result of [15, Theorem 1], we can char-
acterize the maximum transmission delay needed to support
the convergence of error vector ex(t)to the zero vector in
following corollary.
Corollary 1. The convergence of the error vector ex(t)in (10)
to the zero vector is asymptotically stable if the transmission
delay 4τ(t)of the wireless links between these two following
UAVs in the swarm satisfies:
4τ(t)≤τx=
1
λmax(C M 2M1MT
1MT
2CT+CM 2M2MT
2MT
2CT+2kI),
(13)
where k >1,Cis a positive definitive matrix meeting C(M1+
M2) + (M1+M2)TC=−I4×4, and λmax(·)represents the
maximum eigenvalue of the corresponding matrix.
Similar to the analysis in Corollary 1, we can find the delay
requirement τywhich can guarantee that the convergence of
error terms at y-axis to the zero vector is asymptotically stable.
In this case, to guarantee that the error terms of the following
UAVs on x and y axes converge to zero and the swarm of
UAVs forms the target formation, the maximum allowable
wireless transmission delay experienced by the receiving UAV
should be min(τx, τy).
B. Reliability Analysis of the Wireless System
To characterize the performance of the wireless system,
we introduce a notion of reliability for the wireless system.
In particular, we can use stochastic geometry to derive the
mathematical expression for the reliability of the wireless
network. Different from our work in [16], we consider that
the distribution of the interfering UAVs follows a 2D-PPP. In
the following lemma, we use stochastic properties from the
2D-PPP and calculate the reliability.
Lemma 1. If the distribution of the interfering UAV follows
a 2-D PPP with density λ, the reliability of the wireless link
from UAV jto UAV i,i6=j, i, j ∈ {2,3}, can be defined as
P rj,i≈
β
X
k=1
(−1)k+1β
kexp
−kη 2S
ωmin(τx,τy)−1d−α
j,i
Pt
σ2
Li
kη 2S
ωmin(τx,τy)−1d−α
j,i
Pt
,(14)
where η=β(β!)−1/β, and
Li(n) = exp −2π λ Z∞
01−1
1 + nPtr−αrdr.(15)
Proof: The basics of the proof follow from [16] and are
omitted here due to space constraints. However, the proof
of the Laplace transform in (15) is different and provided as
follows:
Li(n) =EΦ"exp −nX
c∈Φ
Ptgc,i(t)(dc,i (t))−α!#
=EΦ"Y
c∈Φ
Egc,i exp −nPtgc,i(t)(dc,i (t))−α#
(a)
=EΦ"Y
c∈Φ
1
1 + nPtd−α
c,i #
(b)
= exp −2πλ Z∞
01−1
1 + nPtr−αrdr,(16)
where Φdenotes the set of interfering UAVs around the swarm,
(a) follows from the assumption of Rayleigh fading channel
and the channel gain gc,i(t)∼exp(1), and the probability
generating function (PGFL) of 2D-PPP [17] is used to prove
the changes in (b) .
TABLE I
SIMULATION PARAMETERS.
Parameter Meaning Value
a2,b2,ˆa2,ˆ
b2Associated gains of UAV 2 1,1,1.5,1.5
a3,b3,ˆa3,ˆ
b3Associated gains of UAV 2 1,1,1.5,1.5
kCoefficient of nondecreasing function 1.01
mNakagami parameter 3
αPath loss exponent 3
σ2Noise variance −174 dBm/Hz
SPacket size 3200 bits
ωBandwidth 20 MHz
0 2 4 6 8 10 12
Time (s)
-6
-4
-2
0
2
4
6
8
Spacing error (m)
/1,2
x/1,3
x/2,3
x/1,2
y/1,3
y/2,3
y
(a) Spacing errors over time.
0 2 4 6 8 10 12
Time (s)
-2
-1
0
1
2
3
4
Velcoity error (m/s)
z2
x
z3
x
z2
y
zy
3
(b) Velocity errors over time.
Fig. 2. Stability validation for a swarm of three UAVs when using the
maximum allowable transmission delay derived in Corollary 1.
IV. SIMULATION RESULTS AN D ANALY SIS
For our simulations, we first validate the results derived in
Corollary 1. Based on Lemma 1, we then study the impact
of interference on the reliability performance of the wireless
network and finally obtain the design guideline of formulating
a stable triangle formation for a swarm of three UAVs. All
simulation parameters are summarized in Table I. Without
loss of generality, we assume that the two following UAVs
have the same control gains, given in Table I. Using the
parameter settings in Table I for Corollary 1, we can find
that the maximum allowable transmission delay to avoid the
instability of the control system is 18.2ms.
We first corroborate the analytical result in Corollary 1
on the stability of the control system under the derived
transmission delay threshold. In particular, we model the
uncertainty of the wireless channel pertaining to the wireless
0 2 4 6 8 10
Spacing target (m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Reliability
6 = 10 # 10-2
6 = 5 # 10-2
6 = 1 # 10-2
X: 2.8
Y: 0.9031 X: 4
Y: 0.901 X: 9
Y: 0.8996
Fig. 3. Reliability performance of systems with different densities of
interfering UAV when spacing target increases.
communication links in the swarm of UAVs as a time-varying
delay in the range (0,18.2ms). The following UAVs are
initially assigned with different velocities from the target
velocity and random locations. Here, the leading UAV flies
with speed components ¯vx= 5 m/s and ¯vy= 5 m/s, and the
target spacing between UAVs are ¯x1,2= 3 m, ¯x1,3= 4 m,
¯x2,3= 1 m, ¯y1,2= 4 m, ¯y1,3= 3 m, and ¯y2,3=−1m. Fig.
2(a) shows the time evolution of the spacing errors. We can
observe that the spacing errors at x-axis and y-axis for both
following UAVs will eventually converge to 0. Also, in Fig.
2(b), we can observe that the velocity errors will converge to
0when time passes by. Thus, by choosing the maximum delay
derived in Corollary 1, we can ensure that the stability of the
swarm of UAVs is guaranteed and the target formation can be
formulated.
Fig. 3 shows the reliability performance of the wireless
network with different densities of interfering UAVs when
the spacing target increases. As observed from Fig. 3, when
the spacing target between two following UAVs increases,
the reliability of the wireless network will decrease. For
example, for a system with density of interfering UAVs
λ= 5×10−2UAV/m2, the reliability is around 35% when the
spacing target is 10 m. However, when the spacing target is
4m, the reliability is 90.1%. Moreover, we can obtain a design
guideline on how to guarantee a stable UAV formation from
the results shown in Fig. 3. In particular, to guarantee that the
reliability of the wireless system exceeds a threshold, we need
to properly choose the target spacing between two following
UAVs in the swarm. As shown in Fig. 3, for a system with
λ= 10×10−2UAV/m2, the target spacing should be chosen a
smaller value than 2.8m so that the reliability performance can
exceed 90%. Also, for a system with λ= 5 ×10−2UAV/m2,
the corresponding target spacing value should be smaller than
4m to reach a reliability of 90%. Moreover, when the density
is chosen as λ= 1 ×10−2UAV/m2, the spacing target should
be smaller than 9m. This is due to the fact that the strength
of the receiving signal will decrease and the delay of the
communication link will increase when the spacing increases.
V. CONCLUSION
In this paper, we have proposed a novel approach to jointly
design the control and communication system of a cellular-
connected swarm of UAVs. Based on the integrated commu-
nication and control strategy, we have performed a control
system stability analysis and derived the delay threshold which
can prevent the instability of the swarm of UAVs. We have
used stochastic geometry to derive the mathematical expres-
sion for the reliability of the wireless system, defined as the
probability of meeting the control system’s delay requirements.
Simulation results have shown that leveraging the synergies
between control and wireless systems can result in a stable
operation of a swarm of UAVs.
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