Air Defense Planning from an Impact of a Group of Unmanned Aerial Vehicles based on Multi-Agent Modeling

Abstract

The paper discusses the methodology of forming an air defense plan to counteract a group of drones based on multiagent modeling. It is shown that the application of traditional planning methods does not take into account the peculiarities of the defense of objects against largegroups of air targets in case of their simultaneous application. The use of a multiagent paradigm for modeling is considered, which considers the defense process as an interaction of two groups of agents: attack and defense. The air situation model is based on the application of agents with simple control methods and the use of cohesive and repulsive functions. The air defense model includes adequate air defense agents' response to air targets. The conclusion about the possibility of multi-agent air defense planning was confirmed by modeling of an infrastructure object defense from attack of a group of drones.

Full text

Pavlo Shchypanskyi et al.,International Journal of Emerging Trends in Engineering Research, 8(4), April 2020, 1302 - 1308
1302

ABSTRACT
The paper discusses the methodology of forming an air
defense plan to counteract a group of drones based on
multiagent modeling. It is shown that the application of
traditional planning methods does not take into account the
peculiarities of the defense of objects against large groups of
air targets in case of their simultaneous application. The use
of a multiagent paradigm for modeling is considered, which
considers the defense process as an interaction of two groups
of agents: attack and defense. The air situation model is based
on the application of agents with simple control methods and
the use of cohesive and repulsive functions. The air defense
model includes adequate air defense agents' response to air
targets. The conclusion about the possibility of multi-agent air
defense planning was confirmed by modeling of an
infrastructure object defense from attack of a group of drones.
Key words : Air Defense, Drone, Group Behavior,
Multi-Agent, Planning, Unmanned Aerial Vehicle.
1. INTRODUCTION
Over the last decade the number of small drones (UAVs)
applications has increased rapidly. At the same time, the
smallest UAVs (drones) are becoming more intelligent and
technically sophisticated. Not surprisingly, in this case, they
can increasingly be used not only with good intentions but
also for terrorist attacks. Drones, simple and cheap, are now
available to a variety of armed groups. The largest-scale drone
attack was launched in September 2019. Its target was large
oil refineries in Saudi Arabia. As a result of the attack, oil
production has fallen by 5.7 million barrels a day, which is
5% of world production, and its price has jumped by 10% [1].
Network coordination technologies now allow terrorists to use
not only single drones, but also their groups, consisting of
dozens of units coordinated across time and space. This
further complicates the task of counteracting such UAV
groups in protecting critical infrastructure as it requires the
concerted management of a large number of forces and
resources.
1.1 Problem Statement
Various mathematical methods can be used for air defense
planning of an infrastructure object: operations research,
probability theory methods, scheduling theories,
mathematical analysis, game theory, statistical analysis,
statistical modeling, etc. [2]. However, the main disadvantage
of such methods is the overly generalized presentation of the
entire “UAV Group - Air Defense” system, which negates the
final result and renders the plan inappropriate. Therefore,
there is a need to use more detailed “multi-agent” game
modeling methods. Submission of individual elements of the
system in the form of independent “agents” allow to analyze
the behavior of each of the studied objects in more detail and
to plan the “defense agents” application more rationally.
A common problem of air defense planning for an important
infrastructure object is the need to forecast UAV group
actions. The specific variant of the air defense counteraction
to a group of drones will depend on the possible location of
individual UAVs in the space above the infrastructure object.
Therefore, it is obvious that the overall planning task will be
based on two models: 1) the model of the air situation
forecast, and 2) the model of air defense counteraction.
1.2 Related Works Overview
In order to develop a model of the air situation forecast, the
UAV team should be considered as a set of agents that
coordinate their actions to fulfill a common goal. By
interacting locally, intellectual agents – UAVs create
so-called collective intelligence that is capable of
self-organization and complex behavior, even if each agent's
Air Defense Planning from an Impact of a Group of Unmanned Aerial Vehicles
based on Multi-Agent Modeling
Pavlo Shchypanskyi
1
, Vitalii Savchenko
2
, Oleksii Martyniuk
3
, Ihor Kostiuk
4
1Deputy Head of Ivan Cherniakhovskyi National Defense University of Ukraine, Kyiv, Ukraine,
info@nuou.org.ua
2Director of Cybersecurity Institute, State University of Telecommunication, Kyiv, Ukraine, savitan@ukr.net
3Associated Professor, Aviation and Air Defense Department of Ivan Cherniakhovskyi National Defense
University of Ukraine, Kyiv, Ukraine, o.r.martyniuk@gmail.com
4Postgraduate Student, Aviation and Air Defense Department of Ivan Cherniakhovskyi National Defense
University of Ukraine, Kyiv, Ukraine, kostiuk1306@ukr.net
ISSN 2347 - 3983
Volume 8. No. 4, April 2020
International Journal of Emerging Trends in Engineering Research
Available Online at http://www.warse.org/IJETER/static/pdf/file/ijeter59842020.pdf
https://doi.org/10.30534/ijeter/2020/59842020

Pavlo Shchypanskyi et al.,International Journal of Emerging Trends in Engineering Research, 8(4), April 2020, 1302 - 1308
1303
strategy is simple enough. The first publications in this field
refer to the research of Craig Reynolds. Observing bird’s
behavior, he proved that the interaction of birds in a flock
requires only a few simple rules of behavior [3]. In [4]
theoretical bases of application of robotic groups are stated.
Studies [5]–[7] describe some particular cases of constructing
spatial group formations based on information about a limited
range of neighbors. Model [8] describes the movement of
search agents in the decision support system. The “Diffusion
Bomb Task” [9] gives an idea of how to defeat an enemy air
defense system (air defense system) by an autonomous group.
[10] describes the UAV group motion model, which most
fully complies with the principles of decentralized
management, is easily scalable and, at the same time, easy to
apply.
The main approaches to air defense organization are laid
down in guidance documents such as ATP 3-01.8 Techniques
for Combined Arms for Air Defense [11] and Joint
Publication 3-01 Countering Air and Missile Threats [12].
However, these documents do not disclose options for
modeling of the air defense counteraction, leaving these
issues for the decision of commanders. In turn, individual
counteraction models are reported in [13], although without
the possibility of numerical estimation of counteraction
parameters. More detailed models can be seen in [14], which
include Tracking models and Bayesian models for target
recognition. At the same time, such approach is not sufficient
to plan the defense of an object in the case of a group UAV
strike. [15] discusses a multi-agent approach to missile
defense planning. At the same time, agent activities are only
implemented for planning procedures without taking into
account the UAV group parameters. The procedures for
planning air defense in real time are well modeled in [16]. At
the same time, the main criterion for such planning is only the
“non-conflict of the plan”, which is inaccessible when
protecting important objects. The best method for combining
with the multi-agent planning model of the air situation in
terms of planning is the method described in [17], which
provides for the deployment of an air defense system
depending on the variant of actions of the group of aircraft. At
the same time, some elements of this model need to be refined.
The purpose of the article is to develop a methodology for
forming an air defense plan for a critical infrastructure object
from a group of unmanned aerial vehicles based on
multi-agent modeling.
2. THE MODEL FOR AIR SITUATION FORECAST
2.1 Multi-Agent Approach to Air Situation Modeling
UAV group application leads to the proportional growth of
information transmitted through the control channels in
dependence from the UAVs number. Therefore, developers
use decentralized control methods, which minimize the
transmission of information in the control channels and
manage the group as the only “integrated” UAV. Group
control consists of two independent tasks: the decomposition
of a group task into individual performers and the concerted
execution of a group task in space and time. From the point of
view of defense, the spatial position of individual drones is the
most significant factor in the planning of defense actions.
Therefore, to form a defense plan based on multi-agent
modeling, it is most appropriate to take as a basis the problem
of the spatial position of the UAV group.
The group R consisting of N UAVs is considered. Each UAV
ri ∈ R (i=1…N) must be capable of performing the following
functions: determining its location (absolute or relative);
keeping in touch with its neighbors in the local group within
the low-power transmitter range dadj; dynamic (re-)planning
of its own route based on the information received.
The task of the group, within the scope of this article, is to
move from the start point with Xbase coordinates to the Xaim
destination, and each UAV must be informationally
connected to the group and be able to avoid interference of
neighbor UAVs and enemy active objects.
2.2 UAV Group Movement
The coherent group motion model is based on the potential
method, which determines that each UAV is drawn to its
destination and to the neighbors of the local group (which are
recognized by onboard sensors). In addition, each UAV repels
obstacles and neighbors to ensure flight safety. In general, the
model can be represented in vector form:
i i i i i
aim coh rep AAD
V V V V V   
    
, (1)
where
i
V

– the resulting velocity vector of UAV ri;
i i
aim coh
V ,V
 
– velocity vectors of approaching to the target and
neighbors respectively; i i
rep AAD
V ,V
 
– velocity repulsion
vectors from neighbors and obstacles, respectively.
Let's look in detail at the first component
i
aim
V

of model (1),
which is responsible for moving the UAV to the target. Fig. 1
shows two UAVs and their trajectories from the start point to
the destination point with coordinates (30,10).
Figure 1: The trajectories of the movement of two UAVs
to the target

Pavlo Shchypanskyi et al.,International Journal of Emerging Trends in Engineering Research, 8(4), April 2020, 1302 - 1308
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The motion of each UAV in this case is described by a system
of equations:


 
 
 
 
 
1
1
0
0
i
aim aim
i
ii
aim
aim aim
i
i base
i base
x t k d
t x t
z t k d
Vt z t
x x
z z


 
 


 
 





 (2)
where


base base base
X x ,z – coordinates of the starting
point;








i i i
X t x t ,z t
 – current UAV coordinates;


aim aim aim
X x ,z – target point
coordinates;
 
 
 
 
2 2
2aim aim i aim i aim
d k x t x z t z     – the
current distance between the і-th UAV and point
aim
X;
1 2
aim aim
k ,k – the model parameters responsible for the
speed-of-destination module and the deceleration when the
target is reached, respectively.
Dependencies of velocity projections on time according to the
parameters
1 2
aim aim
k ,k are shown in Fig. 2-4.
Figure 2: 5.0k,1k 2aim1aim 
Figure 3: 10k,1k 2aim1aim 
Figure 4: 10k,2k 2aim1aim 
2.3 UAVs Action Forecast
UAV action in a group involves a role distribution. So today,
more and more actions of drone groups are reminiscent of the
actions of groups of people or military formations. Such
groups have their own intelligence, radio-electronic
jamming, impact forces, and others. In this case, the agents
which perform the main task will have sufficient information
about the forces that opposes them. Thus, UAVs will know in
advance the location of the air defense facilities and will be
able to bypass them.
Therefore, we include in the model (1) a fourth component
i
AAD
V

, describing the circumvention of the area of damage by
air defense. Jointly the first and fourth components of the
model give the result shown in Fig. 5. Two UAVs go to the
target bypassing the enemy air defense zones.
Figure 5: The trajectories of the movement of two UAVs to
the target, taking into account the circumvention of enemy air
defense zones
In this case, the model of the UAV movement will look like
i i i
aim AAD
V V V 
  
. The vector of the velocity of repulsion of
UAV ri from the set of zones of enemy air defenses is supplied
by the system of equations:

Pavlo Shchypanskyi et al.,International Journal of Emerging Trends in Engineering Research, 8(4), April 2020, 1302 - 1308
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

 
nAAD
1
nAAD
1
AAD
AAD
iAAD
P
i
iaia
AAD iAAD
P
i
aia
dx t k
dt
dt x d
Vdz t k
dt
dt z d



 



 




 (3)
where nAAD – the number of enemy air defense zones;


a a a
X x ,z
 – coordinates of the center of the impact area;
 
 
 
 
2 2
a aia i i
d x t x z t z    – current distance
between UAV ri and the impact area
a
X
;
AAD AAD
k ,P –
model parameters that are responsible for the radius of the
impact area and the rate of repulsion from it.
Components two and three
i i
coh rep
V ,V
 
models (1) provide
flight safety and information coherence for the group at the
same time. The attraction to neighbors does not allow UAV to
exceed the distance of the transmitter dadj, and repulsion –
ensures flight safety by preventing dangerous distance
between neighboring UAVs.
The results of simulation of motion of two UAVs with respect
to joint attraction and repulsion are shown in Fig. 6-8.
Figure 6: The trajectories of motion of two UAVs (r1, r2) to
the target with regard to information coherence dadj <12 and
bypassing obstacles
Figure 7: Projections of UAV velocities r2
Figure 8: The current distance between UAVs r1 and r2
The cohesion and repulsion in model (1) is described by the
following systems of differential equations:
nUAV
1
nUAV
1
coh
coh
i coh
P
i
jijicoh i coh
P
i
jij
dx (t ) k
dt
dt x d
Vdz (t ) k
dt
dt z d














 , (4)
nUAV
1
nUAV
1
rep
rep
rep
iP
i
jij
irep rep
iP
i
jij
k
dx (t )
dt
dt x d
Vk
dz (t )
dt
dt z d



 




 





 , (5)
where nUAV – number of neighbors;
i j
X ,X
– coordinates
of interacting UAVs;
coh coh
k ,P
– model parameters
responsible for the distance and speed of cohesion to
neighbors;
rep rep
k ,P
– model parameters responsible for
distance and repulsion rate from neighbors;
   
 
   
 
2 2
ij cr i j i j
d k x t x t z t z t
 
       – the
current distance between the i-th and the j-th UAV;
cr
k
–
model parameter responsible for acceleration in repulsion and
deceleration in cohesion to neighbors;

– accidental
measuring error of distances between UAVs ri and rj.
The ability to scale the model is confirmed by the simulation.
The results of application of the group with N = 20 UAVs are
shown in Fig. 9. The start of the UAVs is in the square
(0,0)-(5,5), the target point has coordinates (20,20). At the
30th step of model time, there is a distribution of the group
around the target point, which is approaching to equal
distribution.

Pavlo Shchypanskyi et al.,International Journal of Emerging Trends in Engineering Research, 8(4), April 2020, 1302 - 1308
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Figure 9: The trajectories of the movement of twenty UAVs
3. THE MODEL OF MULTI-AGENT AIR DEFENSE
Planning of the air defense deployment is a process that
requires consideration of many factors, including terrain, type
of enemy attack, enemy purposes, air raids, trajectory of
enemy's flight and air defense tactics, intelligence capabilities
etc. In the case of counteracting a group of small UAVs for air
defense of an important infrastructural object, the topology of
the air defense fascilities on the terrain will be extremely
important. The specific position of every counter mean must
take into account the particularities of the object itself and the
surrounding area.
In short, the problem of planning the air defense of an
infrastructure object is the correct deployment of a certain
amount of air defense fascilities in optimally selected
locations around the designated area on the ground. Attack
and defense are two aspects of one problem, this is why the
multiagent attack model should provide a similar multiagent
air defense model.
The article assumes that the object is protected by a system
that includes:
- air defense missile and artillery complexes including fully
automated turrets with motion detection [18];
- radar stations;
- control point of the air defense system.
In this case, each element of the air defense system can be
characterized by different performance indicators, in
particular:
- effective range of impact dt, wherein t is the number of the
type of a separate air defense system;
- the average probability of impact for the defense system st.
3.1 Model of Deployment of Air Defense System
Facilities
Elements of an object's air defense system can be placed at
several predefined deployment points. The set of possible
deployment points is determined in advance based on prior
information (reconnaissance). The following features are
taken into account in this process:
- parameters of the terrain around each deployment point;
- engineering infrastructure of the area.
Only one element of air defense system can be deployed at any
single deployment point from D – set of all possible
deployment points.
3.2 Model of Interaction of UAV Agents with Air Defense
Agents
The content of the air defense plan for an infrastructure object
should include measures to counteract the UAV group air
raid. Applying a multi-agent approach, let's determine that a
separate air defense (missile or artillery) unit must be
assigned to each unit of attack (UAV). Thus, the overall
operation of the system can be described as the interaction of
UAV agents with agents of the air defense system.
Choosing the best deployment points for a defined number of
air defense means selecting pairs that include:
(1) the deployment point number of the air defense facility
from the set of valid deployment points and
(2) the number of air defense facility type assigned to that
deployment point that maximizes a specific function of the
performance criterion (evaluation).
To evaluate the effectiveness of the assignment, it is assumed
that this evaluation function must consider two factors:
- potential air defense deployment points should be selected so
that the distance from the point to the center of the object
being defended is maximized (the earlier the enemy's air
target is impacted, the less likely the mission's success is for
that air target; moreover, it is possible to hit the air target
repeatedly);
- the choice of the specific point of deployment of the air
defense facility must take into account the effectiveness of the
air target hit by the air defense facility;
- the choice of deployment points for air defense facilities
should take into account the expected distribution of the
attack probability, that is, the uneven appearance of UAVs in
different areas on the approaches to the object.
The following function, which selects a pair (the point of
deployment of the air defense facility and the specific air
defense facility), meets these requirements:

Pavlo Shchypanskyi et al.,International Journal of Emerging Trends in Engineering Research, 8(4), April 2020, 1302 - 1308
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 
 
1
; ; 0; 1 ;
; 1 ;
1
N
t n jnt jnt n
n
jnt
s p z z p n ,N
d j,t
n ,N z .
j D, t ,T .

    



    


 

(6)
where zjnt – indicator of combat ability (zjnt = 1, if there is a
possibility of targets impact in a certain area and zjnt= –

otherwise); pn – the probability of hitting by the enemy from п
direction (the UAV agent is in the zone п); st – efficiency
(probability of impact) of the system t; N – the total number of
impact areas by UAVs.
The choice of the best points for the deployment of air defense
facilities, is based on optimization by the matrix of
assignments jt
J T
V v

 
  , the elements of which have the
following meaning:
0 air defense mean is not assigned to point
1 air defensemean is assignedto point
jt
, t j;
v, t j.


 (7)
The solution to the problem is to find some matrix
*jt
J T
V v

 
  , which maximizes function
 
 
1
T
* *
jt
j Dt
f V v d j,t
 
  . (8)
3.3 An Algorithm for Selecting the Best Points to Deploy
To solve the optimization problem (8), we propose the
following algorithm for deploying air defense facilities to
cover an important infrastructure object.
1. Determining the center of the defense area of an important
object S.
2. Modeling UAV routes and identifying the most vulnerable
areas of attack (formulas (2)–(5)).
3. Identification of potential UAV meeting areas by means of
air defense.
4. Determination of allowable deployment points for air
defense equipment.
5. Determination of effective defeat points for air targets by
air defense means of specific types deployed at those points
where impact of air targets is possible (zjnt = 1).
6. Determining the value of the evaluation function d(j,t) for
the following admissible pairs: the admissible points of
deployment of the means and the number of the type of means
of air defense in accordance with formula (6).
7. Selecting the best deployment points according to the
formula (8).
3.4 An Example of Multi-Agent Interaction of Air Defense
with UAVs
To evaluate the capabilities of the multi-agent approach, we
will perform simulations according to the already considered
example (Fig. 9). The results of the application of the group of
N = 20 UAVs and T = 8 air defense systems for an object
defense are shown in Fig. 10.
Figure 10: Results of air defense modeling
The start of the UAV is still in the square (0,0) (5,5), the
target point has the coordinates (20,20). At the 30th step of
model time, there is a distribution of a group around a target
surrounded by air defenses located at points with coordinates:
(18,18), (18,20), (18,21), (20,22), (22, 21), (20,18), (21,21),
selected by the optimization algorithm.
This demonstrates the possibility of a multi-agent approach to
planning the air defense of infrastructure. The advantage of
the method is that iterations can investigate a significant
number of attack options and, accordingly, choose the optimal
distribution of air defense to repel the attack.
4. CONCLUSION
Increasing complexity of modern UAVs has led them to be
increasingly used by terrorist groups for illegal activities. The
general problem of planning the air cover of an important
infrastructure object is the need to anticipate the actions of the
UAV group in the area of the object. Air defense planning is
based on the optimal deployment of air strikes against terrain.
The use of a multi-agent approach makes it possible to
determine the most feasible option for deploying air defense
in pre-selected potential positions. Thus, on the basis of the
multi-agent approach, the technique of forming a plan for air
cover of a critical infrastructure object from a group of
unmanned aerial vehicles is implemented.

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