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Pavlo Shchypanskyi et al.,International Journal of Emerging Trends in Engineering Research, 8(4), April 2020, 1302 - 1308

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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

1304

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:

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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.

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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:

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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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