arXiv:1610.04091v1  [cs.SY]  13 Oct 2016
1
Optimizing Communication and Computation for
Multi-UAV Information Gathering Applications
Mason Thammawichai, Sujit P. Baliyarasimhuni, Eric C. Kerrigan and Jo˜ao B. Sousa
Abstract
Mobile agent networks, such as multi-UAV systems, are constrained by limited resources. In particular, limited energy affects
system performance directly, such as system lifetime. It has been demonstrated in the wireless sensor network literature that the
communication energy consumption dominates the computational and the sensing energy consumption. Hence, the lifetime of the
multi-UAV systems can be extended significantly by optimizing the amount of communication data, at the expense of increasing
computational cost. In this work, we aim at attaining an optimal trade-off between the communication and the computational energy.
Specifically, we propose a mixed-integer optimization formulation for a multi-hop hierarchical clustering-based self-organizing
UAV network incorporating data aggregation, to obtain an energy-efficient information routing scheme. The proposed framework
is tested on two applications, namely target tracking and area mapping. Based on simulation results, our method can significantly
save energy compared to a baseline strategy, where there is no data aggregation and clustering scheme.
I. INTRODUCTION
Inexpensive mobile agents, such as unmanned aerial vehicles (UAVs), are useful for several remote monitoring applications
such as agriculture [1], geology [2], ecology [3] and forestry [4]. The viability of UAVs for scientific and non-military
applications are due to reduced cost of the UAVs, low sensor cost and ease in handling. Typically, these applications are of
large scale and the mission time can be shortened by introducing multiple UAVs.
Central to these applications is the necessity to have a human-in-the-loop (HITL) capability that increases situational
awareness and operator autonomy to modify missions dynamically. For HITL, UAVs have to gather and disseminate information
periodically to the operator who may be located at a distant (base station) from the operational arena. Typical information
required at the base station is aerial footage [5], which is a communication intensive operation consuming considerable energy.
Unfortunately, low cost UAVs have limited flight time due to battery/fuel capacity. Hence, there is a need to find different
mechanisms by which flight time endurance can be increased. One way is to use gliders that take advantage of the updrafts
to soar for long endurance [6]. However, during soaring it is very difficult to maintain a good resolution of the terrain due to
varying UAV height for mapping or surveillance applications. Instead, we propose to optimize the energy consumed by various
units in a given aircraft to increase the flight time and hence the UAV team mission time.
For many applications [1], [4], it is necessary that a UAV must fly at a constant speed and maintain a prescribed height.
Under these conditions, the major energy consumption units are propulsion, sensing, computation and communication. On
average, the power consumed during flight is approximately constant. The sensing and the computational units also consume
constant power. However, the energy expended by the communication depends on (i) the amount of data to be transmitted,
(ii) the distance between a vehicle and the base station and (iii) the number of vehicles transmitting data to the base station.
Moreover, the communication cost is far greater than the sensing and computational energy. For example, a typical sensor
node consumes 1 nJ-1 µJ/sample, roughly 1 pJ/instruction for computation, while communicating via radio frequency (RF) at
the cost of 100 nJ-50 µJ per bit [7]. Hence, it is better for the UAVs to cooperate with each other to minimize the team
communication energy by performing computation on-board such that the amount of data to be transmitted is minimized. That
is, optimally selecting (a) which vehicles should be the computing nodes and (b) determining how many vehicles are required
to communicate with the base station. In this paper, we propose a general Mixed Integer Nonlinear Program (MINLP) that
determines an optimal solution to (a) and (b).
A. Related Work
Similar to our Multi-UAV information gathering problem, the goal of a Wireless Sensor Network (WSN) is to maximize
network lifetime while delivering raw data to the sink (base station) [8]. In order to maximize the lifetime of a network, data
aggregation techniques have been proposed for WSNs where some computations are performed within the node to reduce the
communication cost. It has been shown that by using a sensor node as a communication relay/aggregator, an energy-efficient
Mason
Thammawichai
is
with
the
Department
of
Aeronautics,
Imperial
College
London,
London
SW7
2AZ,
UK.
m
E-mail:
m.thammawichai12@imperial.ac.uk
Sujit P. Baliyarasimhuni is with the Department of Electronics and Communications Engineering, Indraprastha Institute of Information Technology, Delhi,
New Delhi, 110020, India. Email: sujit@iiitd.ac.in
Eric C. Kerrigan is with the Department of Electrical & Electronic Engineering and the Department of Aeronautics, Imperial College London, London SW7
2AZ, UK.Email: e.kerrigan@imperial.ac.uk
Jo˜ao B. Sousa is with the Department of Electrical and Computer Engineering, University of Porto, Portugal - 4200-465. Email: jtasso@fe.up.pt
2
communication strategy can be obtained [9], [10]. Data correlations between different sensor nodes can be exploited to minimize
the number of sensors sending the data to the base station [11]. A compressed sensing technique to reduce the data volume to
be transmitted was proposed in [12].
Hierarchical Network Routing is also one of the techniques in prolonging a network lifetime. For this approach, the nodes
are grouped into clusters and the cluster-head for each group is selected based on various election algorithms [13]. The cluster
head is responsible for aggregation, compression and forwarding data to the base station. For example, in the Low-Energy
Adaptive Clustering Hierarchy (LEACH) protocol proposed in [14], a stochastic scheme is used to determine whether a node
will become a cluster-head in each decision making round, i.e. the probability that a node will become a cluster head is 1/P,
where P is the desired percentage of cluster heads. The Low-Energy Adaptive Clustering Hierarchy Centralized (LEACH-C)
protocol [15], which is an improvement of LEACH, uses global information of the network to determine an optimal number
of cluster heads via a centralized control at the base station. A chain-based protocol, called Power-Efficient Gathering in
Sensor Information Systems (PEGASIS), where the nodes are only allowed to communicate with nearby nodes and take turns
to transmit data to the base station, was proposed in [16]. A hierarchical data aggregation technique where sensor nodes
were grouped into clusters was proposed in [17]. A local aggregator (LA) for each cluster was selected, then a set of master
aggregators (MAs) were selected based on LAs. To select MAs, an integer program is solved such that the total communication
energy is minimized, while performing minimum aggregation computation, such as finding an average or a maximum. For
this work, we adopt a hierarchical cluster-based data aggregation technique from the WSN literature, but the topology of the
network and the number of MAs are dynamically decided.
Another approach is to have a mobile sensing node collect data from the nodes to reduce the communication overload [18]–
[21]. Since the UAVs are mobile, using another UAV to collect data from the surveying UAVs is not an ideal approach. However,
similar to WSN data aggregation, the UAVs can perform computations on board to produce concise data and periodically transmit
to the base station, as in [22] for an image processing application. Data transmission to the base station can be performed either
directly or through a UAV relay network [23], [24]. Therefore, in this work, we propose a self-organizing network topology
that allows data aggregation as well as a multi-hop information routing pattern.
A UAV with sensing capabilities can be applied to perform target tracking due to its adaptability, scalability and better
performance than a static wireless sensor network. However, most of the work on UAV target tracking applications only focus
on the target tracking accuracy, while the communication and computation energy consumption has been neglected [25]–
[28]. Hence, this work aims to incorporate both the communication and computation energy consumption into a multi-UAV
target tracking application. Target tracking algorithms are based on target state estimation. By combining multiple sensor
readings, which originated from different moments in time and distances from the UAVs, a more accurate state estimate can
be obtained [29]. Precisely, the tracking objective is to maximize the information contribution [29], [30] from each node. In
general, it has been shown that the measurement obtained from the most distant node does not contribute much to the target
tracking accuracy. Therefore, it would be energy-efficient to select only the subset of the UAVs to be tracking nodes. The
problem of deciding a subset of tracking sensor nodes could be formulated as an MINLP as in [31], where the observation
covariance depends on the distance, i.e. the further away from the target, the less accurate the measurement. Therefore, in this
work, we include the information contribution constraint to our optimal control formulation for a target tracking application.
UAVs have been used for mapping applications [1], [32]–[34]. However, the focus of mapping applications using UAVs has
been on improving the accuracy of the acquired images, which could be orthomosaic, classification of vegetation, improving
video transmission range, etc. In some applications, the objective is to determine the minimum energy cost path for UAVs.
In [35], the objective for the UAV is to visit a set of pre-defined target locations. The determined path must minimize the
total energy consumed in visiting the targets. In [36], the objective is to develop multi-UAV exploration strategies under
limited battery constraints. In [37], a multi-UAV cooperative system using behavior was developed to efficiently explore a
region with the constraint that the UAVs have limited energy. In most of the above UAV mapping applications, the issue of
optimizing communication energy to enhance mission time is not considered. In our formulation, we want to optimize the
energy consumed by communication and computation components, so that the mission duration can be increased. This aspect
has not be adequately addressed in the UAV mapping literature.
B. Contribution
This paper proposes a simple optimal control problem for mobile agent systems with the objective of minimizing the
communication and the computation energy. Particularly, we present an MINLP formulation for a multi-hop hierarchical
cluster-based self-organizing UAV network to attain an energy-efficient reporting mechanism. The main contributions of this
work are:
• A general MINLP optimization framework for a multi-UAV network to optimally trade-off between the communication
and the computational energy was presented. That is, to dynamically determine: (i) the optimal number of agents to
communicate to the base station, (ii) the role of each UAV: a sensor, a relay or an aggregator, (iii) the communication
links among the UAVs to obtain an energy-efficient information routing network with data aggregation.
• Our data aggregation network model exploits three benefit characteristics: (i) a self-organizing network, which means
that the topology of the network is dynamically decided at each decision time interval, resulting in a more flexible and
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reliable network, (ii) a multi-hop network, which exploits the shorter communication distance to prolong the lifetime
of the network and (iii) a hierarchical clustering network, which can provide a better performance in terms of energy
consumption, reliability, as well as scalability.
• A generalised data aggregation network model that allows multiple flows of more than one data type within the network.
In other words, our network model can be applied to a heterogeneous mobile computing system, where only the same
data types are allowed to be aggregated/processed, i.e. a system with more than one sensor type.
• Two information gathering applications, namely target tracking and area mapping are addressed by our proposed optimal
control framework to illustrate both the correctness and the effectiveness in trading off communication and computation
energy.
• Simulation results show an energy saving of up to 40% for target tracking and 60% for area mapping when comparing
the performance of our MINLP formulation with a baseline approach, where there is no data aggregation and clustering
scheme.
C. Notations
This section provides summary of all notations used throughout the paper.
Variables:
Symbol Description
N
Set of all UAVs (nodes)
n
Total number of nodes
C
Communication link matrix/vector
c
Communication link assignment
M
Set of all data types
m
Total number of data types
λ
Average data transmitting rate
λ
Sensing rate
ǫ
Sufficiently small constant/energy constant
|G|
Total number of sensors of a data type
a
Aggregator assignment
γ
Aggregator ratio
B
Communication bandwidth
h
Decision time interval length
E
Energy consumption
d
Distance between nodes
e
Energy state vector
φ
Inertial position vector
x
Position in x-axis
y
Position in y-axis
v/V
Speed/speed vector
φ/Φ
Heading angle/Heading angle vector
r
Distance/range
X
State of the system
u
Control input
π
Information contribution
H
Observation matrix
R
Measurement noise covariance matrix
F0
State transition matrix
w0
Process noise vector
Q0
Noise covariance matrix
Z
Measurement vector
ν
Measurement noice vector
K
Distance-independent coefficient
Q
Information matrix
P
Covariance error matrix
ˆq
Information state vector
S
Set of sensor nodes
W
Width of a region
T
Length of a region
4
ζ
Overlap factor
Nℓ
Total number of lanes
ℓ
Lane
ω
Waypoint
τ
Transition boundary
χ
Entry angle
Subscritpts/Superscripts:
Symbol Description
i, j
UAV (node)
0
Source (target) node/initial state
n + 1
Sink node (base station)
z
Data type
c
Communication
s
Sensing
p
Processing
t
Transmitting (section III-A)/top (section V-B)
r
Receiving
β
Path loss exponent
+
Next state
k
Decision making round
κ
Lane index
b
Bottom
d
Desired heading angle
D. Outline of Paper
The rest of the paper is organized as follows: In Section II, the application details are presented. Details on problem
assumptions, system models and variable definitions are given in Section III. The optimal control problem formulation is
presented in Section IV. The optimal control problem is applied to target tracking and mapping applications in Section V as
well as simulation results. We conclude in Section VI.
II. APPLICATION DETAILS
For this project, we are looking at the scenerio where a team of n UAVs is given a mission to either pursue a single target
or survey an area of interest (AOI) and needs to periodically send the data back to the base station.
A. System Assumptions
We will assume that at each decision making time interval, each UAV (node) i ∈N := {1, . . ., n} has the same capability
of sensing, data aggregation and communication functions, where n is the total number of UAVs in the fleet. A UAV can reach
any UAV using one-hop communication. A sensing UAV periodically senses a target/AOI, i.e. information (a data packet) is
generated at a constant rate, and hence, the energy consumed by the sensor is constant. We assume that the UAVs are flying
at constant altitude having constant speed and there are no wind disturbances. The power consumed by the propulsion unit
during level flight is given by the relation [38],
Pprop = CD
C3/2
L
s
2Rg3
ρ
m
3
2
b ,
(1)
where CD is the drag coefficient, CL is the lift coefficient, R is the aspect ration of the aircraft, g is the gravity constant, ρ is
the air density, m is the mass of the aircraft and b is the wing span. As we can see from the relation that for a level flight, all
the quantities associated with Pprop are constant. Further, since we assume that the UAV is flying at a fixed altitude, the lift
and drag cooefficients that depend on the velocity of the aircraft are also constant. Hence we assume that the energy consumed
by the propulsion unit is constant under these assumptions. Since the sensor and propulsion energy consumption is constant,
including this in the formulation does not affect the decision-making. Hence, we do not consider this in our formulation. The
information can be of different types, therefore our model can be thought of as either a single source or multiple sources with
different data types. For simplicity, we will consider a system with only one base station to report the data. Note that extension
to multiple sink nodes (base stations) is relatively straightforward.
5
Sensor
ADC
Processing 
   Unit
Data Storage
Network
MAC
Transceiver
Sensor Module
Processing 
  Module
    Wireless
Communication
     Module
Power Supply
Fig. 1: The architecture of a mobile computing node (adapted from [13])
Sink
sensor 1
sensor 3
sensor 2
relay node
aggregator 1
aggregator 2
Fig. 2: Information Flow in an Aggregation Network Topology
B. UAV as a Mobile Computing Node
For this work, a UAV will be modeled as a mobile computing node, which is composed of three primary modules: a
sensor module, a processing module and a wireless communication module, where interactions between modules are shown
in Figure 1. The detailed description of each module is as follows:
• Sensor Module: The main activities of this module includes sensing, analog to digital conversion (ADC) and signal
modulation.
• Processing Module: The processing module is responsible for data processing, sensor control as well as the communication
protocol.
• Wireless Communication Module: The wireless communication module is used for transmitting and receiving. We will
assume that there exists a medium access control (MAC) protocol, which allows a UAV to communicate with other UAVs
and the base station within a transmission range.
C. UAV Role Assignment
Following the works of [9] and [39], we will assume that the UAVs can be assigned to one or more of the following roles
at each time interval: (i) a sensor, which observes the target/AOI (called node 0), via a sensor and produces the data which
will be relayed to the base station (called node n + 1), (ii) a relay, which simply relays its own data to the next level node
without any processing, or (iii) an aggregator, which receives one or more data from other nodes, then aggregates the data of
the same type to produce a single data point and sends the aggregated data to the next level node.
D. Aggregation Network Topology
Figure 2 illustrates the information flow in an aggregation network topology. In particular, the data obtained from the source
(target/AOI) can be processed within the aggregator or passed along the relay node and routed to the sink (base station). Note
that, in this work, the network topology is dynamic, which differs from others in the WSN literature, i.e. the roles of the UAVs
are decided at each time interval. Moreover, only data of the same type is allowed to be compressed/aggregated.
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III. DYNAMIC MODEL WITH CONSTRAINTS
A. Communication Model and Constraints
Let C := [cijz] denote a communication link matrix, i.e. cijz = 1 if node i transmits data of type z to node j for
i, j ∈N + := N ∪{0, n + 1}, z ∈M := {1, . . ., m}. Note that c0iz = 1 if node i is a sensor of data type z and ci(n+1)z = 1
if node i sends data type z to the base station. The communication link matrix C is subject to
cijz ∈{0, 1},
∀i ∈N +, j ∈N +, z ∈M
(2)
n
X
j=1
c0jz ≥1,
∀z ∈M
(3)
n
X
i=1
ci(n+1)z ≥1,
∀z ∈M
(4)
n+1
X
j=1
cijz ≤1,
∀i ∈N, z ∈M
(5)
ciiz = 0,
∀i ∈N +, z ∈M
(6)
where (3)–(4) guarantee that for each information type there is at least one communication link from a source to a node and
there must be at least one communication link between a node and the base station, respectively. Note that contraint (3) defines
an initial state of the network flow at each decision time interval. Constraint (5) enforces that there is only one communication
link of each data type out of a node. Constraint (6) prevents self communication.
Let λijz ≥0 denote the average rate (packets per second) at which data of type z is transmitted from node i to node j. Note
that λ0jz represents the sensing rate of data type z, assumed to be a constant equal to λz packets per time interval. Following
the definition of the communication link matrix C, λijz needs to satisfy:
λijz = 0 ⇒cijz = 0, ∀i ∈N +, j ∈N +, z ∈M,
(7a)
λijz > 0 ⇒cijz = 1, ∀i ∈N +, j ∈N +, z ∈M.
(7b)
Constraint (7) says that if there is data flow between two nodes, then the link assignment should be active. The constraint (7)
can be implemented as the following inequality constraints:
ǫcijz ≤λijz ≤|Gz|λzcijz, ∀i ∈N +, j ∈N +, z ∈M,
(8)
where ǫ is a sufficiently small positive number and |Gz| is the total number of sensors of data type z. In other words, suppose
λijz ̸= 0, then (8) is true if and only if cijz = 1. Suppose λijz = 0, then (8) is true if and only if cijz = 0.
Denote aiz ∈{0, 1}, ∀i ∈N, z ∈M as the data type aggregator assignment, where by definition
aiz = 1 ⇐⇒
n
X
j=0
cjiz > 1, ∀i ∈N, z ∈M.
(9)
In other words, if there are more than one packets of the same data type transmitted to a node, then the node will act as an
aggregator. Constraint (9) can be written as a set of linear inequalities as follows:
(1 −n)aiz +
n
X
j=0
cjiz ≤1,
∀i ∈N, z ∈M,
(10a)
(1 + ǫ)aiz −
n
X
j=0
cjiz ≤0,
∀i ∈N, z ∈M,
(10b)
where ǫ is a sufficiently small positive number.To guarantee a feasible communication link, the data flow within the node needs
to be conserved, i.e. the incoming data equals the aggregated outgoing data:
m
X
z=1
n+1
X
j=1
cijzλijz =
m
X
z=1
n
X
j=0
cjizλjiz(1 + (γz −1)aiz),
∀i ∈N, z ∈M,
(11)
where 0 ≤γz ≤1 is the aggregation ratio of data type z. Observe that when γz = 1, then there is no data aggregation/processing.
Since the nodes are communicating via wireless network, the channel bandwidth are shared among the nodes. This implies
that communication between two nodes restrains available bandwidth to other neighbor nodes. Therefore, bandwidth limitation
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1
2
3
4
5
Sink
Source
λ
0

 
 
λ
λ
λ
 
	 

λ
λ
λ
λ
131
232
432
6
λ
3 
 

λ
λ
 
λ231
 
λ
λ
λ
 
 
Fig. 3: Aggregation Network Topology Example
should be considered in our formulation as well, i.e. all communication data (number of transmitting/receiving bits) should
not be greater than the channel bandwidth limitation. Specifically, the bandwidth constraints can be formulated as
m
X
z=1
n+1
X
j=1
cijzλijzL +
m
X
z=1
n
X
j=1
cjizλjizL ≤Bh, ∀i ∈N,
(12)
where B is the channel bandwidth (bits per second), h is the decision time interval and L is the packet length (number of bits
per packet).
Finally, we will use an example scenario to show the information flow topology that can be achieved from our model.
Consider Figure 3 where the system is composed of five UAVs that are given a mission to retrieve three different types of
information. Nodes 1, 2 and 4 are sensor nodes, node 3 is both a sensor and an aggregator, while node 5 is a sensor as well
as a relay node. The correlated data obtained from node 1 (λ131) and node 2 (λ231) are processed within node 3. At the same
time, the data obtained from nodes 2 (λ232), 3 (λ032) and 4 (λ432) are also processed within node 3. Specifically, from (11),
the outgoing data flow after the aggregation within node 3: λ351 = (λ131 + λ231)γ and λ352 = (λ032 + λ232 + λ432)γ. Both
processed data streams/packets are relayed to node 5, which are transmitted to the base station. Note that node 5 acts as a
relay node because the data received from node 3 and its own data are of different types.
B. Energy Models
We will adopt an energy consumption model, which has been commonly used in the wireless sensor network literature [40]–
[42]. The total energy in most multi-UAV applications is composed of three terms. The first term is the sensing energy Es,
which is the energy used to sense a target/AOI. We will assume that the energy to sense one bit of information is a constant
equal to ǫs J. The sensing energy consumed by node i within the time interval is
Es
i (c0iz) := ǫsL
m
X
z=1
λzc0iz, ∀i ∈N.
(13)
The second one is the aggregation energy Ep, which is the energy to do data processing. The energy to process one bit of
information is also assumed to be a constant equal to ǫp J. The aggregation energy consumed by node i within the time interval
is
Ep
i (cjiz, λjiz, aiz) :=ǫpL
m
X
z=1
λzc0izaiz+
ǫpL
m
X
z=1
n
X
j=1
cjizλjizaiz, ∀i ∈N.
(14)
The last energy term is the communication cost, which is composed of two parts: the transmitting energy Et and the receiving
energy Er. The transmitting energy depends on the distance between the nodes dij, i.e. Et(dij) := ǫt + ǫrfdβ
ij, where β ≥2
is the path loss exponent, ǫt (J/bit) and ǫrf (J/bit/mβ) are constants. The energy of receiving one bit of information is assumed
to be a constant equal to ǫr J. The receiving energy consumed by node i within the time interval is
Er
i (cjiz, λjiz) := ǫrL
m
X
z=1
n
X
j=1
cjizλjiz, ∀i ∈N.
(15)
8
The transmitting energy consumed by node i within the time interval is
Et
i(cijz, λijz, dij) :=
m
X
z=1
n+1
X
j=1
(ǫt + ǫrfdβ
ij)cijzλijzL, ∀i ∈N.
(16)
The total energy used by node i for sensing a target/AOI, processing information and communication during the time interval
is denoted by
Ei := Es
i + Ep
i + Er
i + Et
i, ∀i ∈N.
(17)
Let ei be the energy stored in the ith UAV at time t, then the remaining energy e+
i at time t + h is given by
e+
i := ei −Ei ≥0, ∀i ∈N.
(18)
C. UAV Dynamic Constraints
The two-dimensional UAV kinetic model is given by:
 ˙xi
˙yi

= f(ϕi, vi, ψi) =
vi cos ψi
vi sin ψi

, ∀i ∈N,
(19)
where ϕi = [xi yi]T is the inertial position, vi is the speed and ψi is the heading of the ith UAV. We will assume that UAVs
fly at a constant speed and heading in the interval [t, t + h] and are subject to the following constraint:
vmin ≤vi ≤vmax, ∀i ∈N,
(20)
where vmin and vmax are lower and upper bounds on speed.
Moreover, since we assume that the UAVs are in one-hop communication range and to avoid collision among UAVs at each
time interval, the following constraints are necessary:
rc > dij ≥rsafe, ∀i ̸= j, (i, j) ∈N × N,
(21)
where rc is a sufficiently large positive number defined as a communication range limit, dij is the distance between two nodes
and rsafe is the safety distance.
D. State Update Equation
Let k denote the kth decision making round at time interval [tk, tk+1], i.e. tk+1 −tk = h. The state Xi and the control
input ui for the ith UAV are defined as
Xi := (ei, ϕi),
∀i ∈N,
(22)
uijz := (c0iz, cijz, λijz, aiz, vi, ψi),
∀i ∈N, z ∈M,
j ∈N ∪{n + 1},
(23)
where X := (X1, X2, . . . , Xn) is the state of the overall system. The components of the overall system control input u are
all uijz, i ∈N, j ∈N ∪{n + 1}, z ∈M.
Obviously, all the variables in the previous sections can be considered as a function of k. Let X(k) denote the state of the
overall system and u(k) denote the system control input at time tk. The overall system state update equation is given by
X(k + 1) = φ(X(k), u(k), k), ∀k,
(24)
where φ can be derived from (18) and (19).
IV. OPTIMAL CONTROL PROBLEM
We formulate the optimal control problem to determine the roles of the UAVs as an MINLP. We apply this formulation to
a multi-UAV target tracking application and a multi-UAV mapping application. The MINLP is solved at each time instant tk.
I) Target Tracking: Though our main objective is to minimize the total energy consumed by all nodes in the system (17), for
the target tracking application the target tracking accuracy should be considered as well. Particularly, this can be incorporated
as a constraint that guarantees a minimum information contribution πmin requirement as
π :=
m
X
z=1
n
X
i=1
c0iz tr{Hi(t)T log (R−1
i
(t))Hi(t)} ≥πmin,
(25)
where π is the information contribution, Hi(t) is the observation model and Ri(t) is the measurement noise covariance. Note
that our definition of information contribution is slightly different from the one defined and used in [29]–[31]. Specifically, we
took the natural logarithm of the inverse of Ri(t) to reduce the decay rate of information contribution in order to match with
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the target tracking application using mobile agents, i.e. the useful information can be obtained within a reasonable distance
between the sensor and the target.
The sensing range limit can be implemented as the following constraint:
c0jz(d2
0j −r2
s) ≤0, ∀j ∈N, z ∈M,
(26)
where d0j is the distance between the node and the target and rs is the maximum sensing range. Constraint (26) states that if
a node is a sensor, then the distance between the node and the target has to be less than the maximum sensing range. Note
that the square of the distance is chosen for an easier implementation.
The multi-UAV target tracking problem can be formulated as the following optimal control problem: Given n UAVs, a target
and a base station, determine a role for each UAV, a communication network link and a UAV trajectory that solves
minimize
u
n
X
i=1
Ei
subject to
(2)–(6), (8), (10)–(21),
(25) and (26)
II) Area Mapping: Given n UAVs, an AOI, a base station and a UAV trajectory, determine a role for each UAV and a
communication network link that solves
minimize
u
n
X
i=1
Ei
subject to
(2)–(6), (8), (10)–(18) and
vi = Vi, ∀i ∈N,
(27a)
ψi = Ψd
i , ∀i ∈N,
(27b)
c0iz = Ci, ∀i ∈N,
(27c)
where Vi is the constant speed of the vehicle and Ψd
i is the desired heading angle of the path. Ci is a pre-determined data type
sensor assignment vector. Also, note that for an area surveying/mapping application, the UAV dynamic constraints described
in Section III-C are not included because we assume that the trajectory of each UAV and the collision avoidance among UAVs
are decided by a path planning controller.
V. APPLICATIONS
This section provides simulation results to illustrate the correctness and effectiveness of our framework in trading off
communication and computation energy consumption in multi-UAV applications. A multiple UAV single-target tracking and
area mapping application are chosen as our demonstration examples. All simulations were simulated on MATLAB [43] and
the MINLP was modelled using OPTI TOOLBOX [44] and solved with SCIP [45].
A. Target Tracking
1) Target and Sensor Models: For a target tracking application, we will follow the work of [31] to set up the optimization
problem to make a decision on a subset of the UAVs to be sensor nodes. The motion of a target will be modelled as a linear
discrete-time Markov process:
X0(t + 1) = F0(t)X0(t) + w0(t),
(28)
where X0(t) is the state vector of a target, F0(t) is the state transition matrix and w0(t) is the process noise assumed to be
zero mean Gaussian noise with covariance Q0(t).
The measurement equation of a sensor is
Zi(t) = Hi(t)X0(t) + νi(t),
(29)
where νi(t) is the measurement noise assumed to be zero mean Gaussian with covariance Ri(t). We will assume that the
measurement noise covariance is a function of the distance between a sensor and a target, i.e. Ri(t) := K(t)dβ
0i(t), where
K(t) is a distance-independent coefficient, and d0i(t) is the distance from a sensor to a target. Moreover, we will also assume
that the measurement noise covariances are uncorrelated between any two nodes.
10
2) Information Filter: For multi-sensor data fusion, we use an information filter [31], [46], which is an inverse covariance
form of the Kalman filter. Let ˆX0(t|t) and ˆX0(t+1|t) denote the target estimated state vector and target predicted state vector,
respectively. Define the information matrix Q(t|t) := P −1(t|t) and Q(t + 1|t) := P −1(t + 1|t), the information state vector
ˆq(t|t) := P −1(t|t) ˆ
X0(t|t) and ˆq(t + 1|t) := P −1(t + 1|t) ˆX0(t + 1|t), where P(t|t) and P(t + 1|t) are the covariances of the
estimation error X0(t|t) −ˆX0(t|t) and the prediction error X0(t + 1|t) −ˆX0(t + 1|t). The prediction and estimation steps are
Estimation:
ˆq(t|t) = ˆq(t|t −1) + HT
i (t)R−1
i
(t)Zi(t),
(30)
Q(t|t) = Q(t|t −1) + HT
i (t)R−1
i
(t)Hi(t),
(31)
Prediction:
ˆq(t + 1|t) = Q(t + 1|t)F0(t + 1)Q−1(t|t)ˆq(t|t),
(32)
Q(t + 1|t) = (F0(t + 1)Q−1(t|t)F T
0 (t + 1) + Q0(t + 1))−1.
(33)
For multi-sensor data fusion, i.e more than one node tracking the target, (30) and (31) are replaced, respectively by
ˆq(t|t) = ˆq(t|t −1) +
X
i∈S
HT
i (t)R−1
i
(t)Zi(t),
(34)
Q(t|t) = Q(t|t −1) +
X
i∈S
HT
i (t)R−1
i
(t)Hi(t),
(35)
where S is a set of sensor nodes.
3) Simulation settings: For simplicity, we consider a small UAV network, i.e. n = 3, which are deployed to track a single
target in a two-dimensional area and needs to periodically report the target state back to the base station. Note that we
consider the single target state as one data type. The base station is at (0,0). The initial positions of the UAVs are at positions
(0,100), (100,0), and (100,100). The target initial position is (20,20). The target state vector X0(t) in (28) is composed of the
target positions in the x and y axes, and velocities in the x and y axes, denoted as vx and vy, respectively. The parameters
corresponding to the target state (28), measurement equations (29) and information filter are [31]:
F0(t) =




1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1



, Q0(t) =




2
0
0
0
0
2
0
0
0
0
0.04
0
0
0
0
0.04



, ∀t
Hi(t) =
1
0
0
0
0
1
0
0

, K(t) =
1 × 10−6
0
0
1 × 10−6

, ∀t
ˆq(1|0) =




0
0
0
0



, Q(1|0) =




1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1.




For all simulations, we let the target velocities be vx = 10 m/s vy = 15 m/s. The UAV parameters [47] are vmin = 10 m/s,
vmax = 30 m/s, the initial UAV energy budget is 10 J, the communication range rc = 500 m, the sensing range rs = 200 m, the
safety distance rsafe = 50 m, the decision time interval h is 1 s. The energy parameters [9] are ǫs = 50 nJ/bit, ǫp = 10 nJ/bit, ǫr = 135 nJ/bit
45 nJ/bit, ǫrf = 0.1 nJ/bit/m2, γz = 0.7, β = 2, L = 1024 bits/packet, λz = 5 packets/time interval and πmin = 6.
4) Simulation Results: We compare the results obtained from the MINLP with a baseline strategy where all sensor nodes
individually communicate with the base station using a single-hop communication protocol. The comparison is performed in
terms of energy consumed per decision time interval [t, t + h] between the MINLP and the baseline strategy. The vertical
axis in Figure 4 represents the system energy consumption per decision time [t, t + h] normalized by the baseline scheme.
Similar to the observations in [48], which studies the impact of bandwidth constraints of the energy consumption of WSN,
our simulation also suggests that the channel bandwidth constraint has an effect on the energy consumption of the system.
This is due to the restriction on the information flow pattern. Specifically, when the bandwidth is limited below the threshold
value of 5 Kbps (not shown on the plot), the MINLP algorithm cannot find a solution that is better than the baseline strategy,
hence no energy saving can be obtained. However, when the channel bandwidth is above the threshold, the MINLP can provide
an optimal strategy that can save energy consumption up to 40% compared to the baseline strategy, as shown in Figure 4.
However, the energy saving improvement cannot be observed with an increase in B > 6 Kbps. Figure 5 shows the aggregator
role assignments of each UAV at each time instance of the simulation, where 1 refers to an active role.
11
0
5
10
15
20
25
0.7
0.8
0.9
1
1.1
Time (s)
Normalised Energy Consumption
 
 
B = 6 Kbps
B = 7 Kbps
B = 8 Kbps
Fig. 4: Normalised total energy consumption for different channel bandwidths with respect to baseline scheme
0
5
10
15
20
25
0
0.5
1
 
 
0
5
10
15
20
25
0
0.5
1
Aggregator Node Assignment
 
 
0
5
10
15
20
25
0
0.5
1
Time (s)
 
 
UAV 2
UAV 1
UAV 3
Fig. 5: Aggregator node assignments at different time steps for channel bandwidth B = 7 Kbps
B. Area mapping
A team of n UAVs are deployed to survey a rectangular region with a length of T meters and a width of W meters using
cameras. The vehicles are subject to communication, sensing and energy constraints. Each UAV has a sensing range of rs
meters determined by the camera resolution and altitude. Typically, mapping applications are performed using a lawn-mowing
pattern and hence we split the rectangular region into lanes of width ζrs, where 0 < ζ ≤1 is the overlap factor. ζ = 1 implies
the distance between the lanes is rs and there is no overlap of sensing regions between the aerial survey of UAVs, while
0 < ζ < 1 implies there is some overlap of the sensor footprint between two adjacent lanes. In terms of area coverage ζ = 1
is the best strategy. However, for mapping purposes, there must be at least 50% overlap between two lanes to create good
mosaics [49]. We assume a linear relationship between the overlap factor and the data aggregation ratio, i.e. ζ = γ, which
means that the higher the overlapping area, the higher the data reduction after data processing. Note that here we assume that
the overlap factor is a constant and the same for all nodes, therefore the subscript z of γ notation is dropped. The number
of lanes are Nℓ:= ⌈
T
2ζrs ⌉+ 1 and each lane is denoted by ℓκ, κ = 1, . . . , Nℓ. The vehicles use waypoint navigation for the
survey and hence each lane ℓκ is represented by two waypoints ℓκ = (ωb
κ, ωt
κ), where, ωb
κ = (xb
κ, yb
κ), ωt
κ = (xt
κ, yt
κ) as shown
in Figure 6. Lane ℓκ can be accurately tracked using any accurate path following algorithm [50].
The time taken by the UAV team to survey the complete region depends on the number of UAVs deployed; when n = 1,
the lower bound on the mission time is WT Nℓseconds. Initially, UAV i is given a lane ℓi, i ∈N in terms of their waypoints
ℓi = (ωb
i , ωt
i). Once the vehicle reaches ωt
i, the lane ℓi+n = (ωt
i+n, ωb
i+n) is assigned. However, we can see that UAV i was
assigned the waypoint sequence (ωb
i , ωt
i) for the first lane while (ωt
i+n, ωb
i+n) was assigned the next lane. If we assigned
(ωb
i+n, ωt
i+n), then the vehicle has to travel from ωt
i to ωb
i+n, which is unproductive travel, since the vehicle expends fuel
without surveying any of the region. Hence, we assign the UAV with an alternating sequence of waypoints.
The desired heading angle ψd
i is determined as
ψd
i =
 arctan(yb
κ −yt
κ, xt
κ −xb
κ)
if ℓκ = (ωb
i , ωt
i)
arctan(yb
κ −yt
κ, xb
κ −xt
κ)
if ℓκ = (ωt
i, ωb
i ).
(36)
1) Simulation Setting: We consider a region of 3000 m×3000m and the base station is located in the middle at (1500, 1500).
The sensing range of the vehicles rs = 100 m, the communication range rc = 500 m and the speed of the vehicles is 10 m/s.
We assume three vehicles are deployed to perform the mapping. The parameters used in the simulation are ǫs = 50 nJ/bit, ǫp =
10 nJ/bit, ǫr = 135 nJ/bit, ǫt = 45 nJ/bit, ǫrf = 0.1 nJ/bit/m2, β = 2, L = 1280 × 720 bits/packet and λz = 5 packets/time
12
UAVs
Base station
Lanes
lane
W
T
Fig. 6: The search area is decomposed into lanes and each UAV is assigned to one lane. Once the UAV completes one lane,
then another lane is assigned.
50
100
150
200
250
50
100
150
200
250
X in meters
Y in meters
τ
Fig. 7: The path is given by waypoint (150,0) and (150,300). The vector field of the vehicle at various locations is shown.
τ = 20 and χ = π/3.
interval. Each UAV communicates to the base station every h = 5 seconds. The vector field based path following algorithm [51]
is selected as the UAV path planning controller. The vector field based path following approach uses a two-fold strategy. When
the vehicle is far away from the desired path, the algorithm directs the vehicle towards the path until the vehicle is τ meters
from the path as shown in Figure 7, where the parameter τ is the transition boundary between moving towards the path and
following the path. The vehicle then transits into following the desired path with an entry angle of χ. The effects of τ and χ
are well studied in [51] and [20]. For all simulations, we use τ = 20 meters and χ = π/3 rad.
1
2
3
(a)
1
2
3
(b)
Fig. 8: (a) No common data between the nodes (b) nodes 1 and 2 have common data of type 0.
For the mapping application, the values for c0iz depend on the distance between the nodes. That is, if the distance is greater
than twice that of the sensing range rs, then we will assume that the sensing data are not related and cannot be aggregated.
In other words, the data are of different types. In order to illustrate how c0iz values are determined at each decision interval,
consider a three vehicle system in Figure 8a where a distance between node i and node j dij > 2rs. For this scenario, there
13
1
2
3
(a)
1
2
3
(b)
Fig. 9: (a) node 2 has common data of type 0 with node 1 and type 1 with node 3 (b) all the nodes have common data of
type 0 and 1.
0
20
40
60
80
100
120
0
0.2
0.4
0.6
0.8
1
Time (s)
Normalized Energy Consumption
 
 
B = 6 Mbps
B = 10 Mbps
B = 13 Mbps
Fig. 10: The normalized total energy of the MINLP compared to the baseline strategy for different bandwidth constraints
having ζ = 0.5.
is no common data type between the nodes due to no overlap of the sensed regions, i.e. z ∈{0, 1, 2}. Therefore, the values
of c010 = 1, c011 = 0, c012 = 0, c020 = 0, c021 = 1, c022 = 0, c030 = 0, c031 = 0 and c032 = 1, which implies that none of the
nodes have common data type.
Now consider the scenario as shown in Figure 8b, where nodes 1 and 2 have a common data type z = 0 and node 3 is
distant from nodes 1 and 2. Therefore, in this case, we have c010 = 1, c011 = 0, c020 = 1, c021 = 0, c030 = 0 and c031 = 1.
Similar to this scenario, if node 2 and 3 have a common data type z = 1, while node 1 is distant from nodes 2 and 3, then
c010 = 1, c011 = 0, c020 = 0, c021 = 1, c030 = 0 and c031 = 1.
Another scenario is where one of the nodes may have two common data types, as shown in Figure 9a in which node 2 shares
data with node 1 and node 3, but node 1 and node 3 are far from each other and do not have common data. In this case, we
set c010 = 1, c011 = 0, c020 = 1, c021 = 1, c030 = 0 and c031 = 1. The last scenario is where all nodes are within 2rs distance
of each other as shown in Figure 9b. In this case, c010 = 1, c020 = 1 and c030 = 1. Thus, depending on the node positions
and overlap regions, the values c0iz are pre-determined at the beginning of each decision interval. For our simulations, we
consider scenario as in Figure 9a for ζ < 0.75, and Figure 9b for ζ > 0.75.
2) Simulation Results: The bandwidth allocated to communicate with the base station plays a key role in determining the
computing nodes. Figure 10 shows the total energy consumption of the MINLP normalised to the baseline strategy for every
h = 5 seconds with an overlap factor ζ = 0.5. When the available bandwidth is less than 6 Mbps (not shown on the plot), the
nodes communicate directly to the base station. Hence, we do not show this effect. However, when we increase the bandwidth,
data aggregation behaviours can be observed. As shown in Figure 10, the energy saving is close to 20% for most of the decision
cycles (for B = 6 Mbps). With further increase in bandwidth to B = 10 Mbps, we can see that there is further increase in
energy saving of 35%. However, with additional increase in bandwidth to B = 13 Mbps, there is no further improvement
in energy saving. As expected, the energy reduction is due to co-operation among the agents, i.e. when the bandwidth is
sufficiently large, more energy-efficient feasible information flow patterns are allowed.
In the mapping application, the overlap factor ζ plays a key role in determining the amount of information that needs to be
transmitted by the aggregator node to the base station. When ζ increases, the agents are close to each other with high overlap.
Therefore, during the mosaic operation, the resultant image size will be smaller compared to the sum of individual images.
In order to validate this hypothesis, we carried out experiments with different overlap factors ζ = 0.3, 0.5, 0.7 and 0.9 for the
same bandwidth of 10 Mbps. In Figure 12, we can see the effect of ζ for a given bandwidth. Specifically, the energy saving
increases as ζ increases. For example, when ζ = 0.9, we can achieve savings up to 60% compared to the baseline strategy.
We further, carry out simulations for 5 agents having the same simulation parameters as above. Figure 13 shows the respective
energy saving when 5 agents perform the survey. With increasing overlap factor, the amount of information to be dispatched
reduces and hence there is a decrease in energy consumption. With increase in number of agents we can see that a trend in
energy conversation similar to that of agent 3 simulation can be seen.
We are not performing simulations with large number of agents (>10) because (i) normally, UAVs are composed of no
14
0
20
40
60
80
100
120
0
0.5
1
1.5
 
 
0
20
40
60
80
100
120
0
0.5
1
1.5
 
 
0
20
40
60
80
100
120
0
0.5
1
1.5
Time (s)
 
 
Aggregator node assignment
UAV 1
UAV 2
UAV 3
(a) B = 6 Mbps
0
20
40
60
80
100
120
0
0.5
1
1.5
 
 
0
20
40
60
80
100
120
0
0.5
1
1.5
 
 
0
20
40
60
80
100
120
0
0.5
1
1.5
Time (s)
 
 
Aggregator node assignment
UAV 1
UAV 2
UAV 3
(b) B = 10 Mbps
Fig. 11: The aggregator node selection at different time steps when the bandwidth parameter is varied for the same overlap
ζ = 0.5.
0
20
40
60
80
100
120
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (s)
Normalized Energy Consumption
 
 
ζ=0.3
ζ=0.5
ζ=0.7
ζ=0.9
Fig. 12: The normalized total energy of the MINLP with reference to the baseline strategy for different overlap factors having
a channel bandwidth of B = 10 Mbps.
0
20
40
60
80
100
120
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time in seconds
Normalized energy consumption
 
 
ζ=0.6
ζ=0.7
ζ=0.8
ζ=0.9
Fig. 13: The normalized total energy of the MINLP (for 5 agents) with reference to the baseline strategy for different overlap
factors having a channel bandwidth of B = 20 Mbps.
15
more than 10 in a real application, which is different from WSN which are composed of a large number of nodes and (ii) if
we were to apply our approaches to a large number of UAVs (10+), then we can adopt a hierarchical approach, where a small
set of UAVs (≤10) are assigned to a single base-station and the operation consists of many base stations. With increase in
number of nodes, the amount of data to be transmitted increases and a single receiver may not be able to handle such high
traffic. Hence, the usual approach especially when imagery data need to be transmitted from UAVs is to assign a receiver to
which a small set of UAVs communicate.
VI. CONCLUSIONS
Cooperation between mobile computing agents enables them to optimize the computation and communication energy
consumption, thereby increasing the system lifetime. We have devised an MINLP formulation that shows lower energy
consumption by incorporating data aggregation and clustering schemes. The MINLP formulation is generic and we utilized
this generality by validation on two data gathering applications, namely target tracking and mapping. We have studied the
effect of different parameters on the MINLP decision-making. Simulation results show that the channel bandwidth has a direct
impact on the energy saving scheme, i.e. sufficient bandwidth is necessary for an implementation of an intelligent information
routing scheme.
The proposed MINLP formulation can be further extended to optimize the energy consumption of various units. One potential
direction is to make a decision on when to communicate to the base station. Currently, we assume that the decision interval is
fixed. However, depending on the amount of data, channel bandwidth and the transceiver energy properties, the decision cycle
can be dynamically selected to optimize the overall energy consumption.
Solving the MINLP efficiently as well as whether to implement the proposed framework in a centralized or distributed
manner could be subjects for future work.
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