Jtam.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

48, 3, pp. 551-566, Warsaw 2010

THE DYNAMIC MODEL OF A COMBAT TARGET HOMING
SYSTEM OF AN UNMANNED AERIAL VEHICLE

Zbigniew Koruba

Kielce University of Technology, Faculty of Mechatronics and Machine Building, Kielce, Poland

e-mail: ksmzko@eden.tu.kielce.pl

Edyta Ładyżyńska-Kozdraś

Warsaw University of Technology, Faculty of Mechatronics, Warsaw, Poland

e-mail: e.ladyzynska@mchtr.pw.edu.pl

Thework presents the concept of the application of an unmanned aerial
vehicle (UAV) used in the process of direct reaching of ground targets
(radio location stations, combat vehicles or even tanks). The kinema-
tic model of UAV motion takes into consideration particular phases of
the mission realised by the vessel, i.e. programmed flight during target
search, follow flight after the encounter of the target as well as during
the process of self directioning onto the target. Control laws for the
automatic UAV combat pilot are presented and the dynamic model of
automatically steered UAV is developed. In the examinations solutions
of analyticalmechanics for holonomic settingswithin the relative system
tightly connected with the moving object are incorporated.

Key words: automatically steered aerial vehicle, control laws, controlled
gyroscope

1. Introduction

All stages of UAV operation are characterised by great complexity. It requ-
ires various technological systems and solutions. The system of UAV control
is of primary importance here. While UAV performs its mission, firstly, the
measurement, evaluation and check of the flight path parameters and techni-
cal systems must be carried out. Secondly, it is necessary to properly control
the flight and the seeking and illumination systems, which is achieved due to
the identification and check of the above-mentioned parameters. The identi-
fication, check and control are all executed either directly by an operator or
automatically.



552 Z. Koruba, E. Ładyżyńska-Kozdraś

The necessity of maintaining two-way (often continuous) communication
with the ground command post is a distinct disadvantage to UAV operation
as the post location might be revealed, although various means are employed
to conceal such communication. In modern UAVs therefore, the autonomy of
their systems in the task of ground target search and tracking plays the key
role. It is required that it shouldbepossible to introduce corrections duringthe
programmedflight or even to change it completely depending on the situation,
e.g. on target detection.

Modern ammunition of the so-called ”precise” kind, like missiles, rockets
and bombs (MRB) are controlled with semi-active homing methods. Such
methods of control of theMRB flight path require target illumination, which
is executed with radar beams or infrared radiation. The latter has been used
more andmore frequently because of well-known advantages it has.

Target illumination is usually performed fromgroundposts or fromthe air,
fromplanes and helicopters. There are a number of disadvantages to this kind
of illumination. It is necessary for the target to be visible. With illumination
from ground posts, the target view can be blocked by natural obstructions.
Moreover, the post can be easily detected and destroyed by the adversary.
Manned planes and helicopters are used to carry out aerial illumination. As
it is necessary to illuminate the target for a certain definite time, the flying
vehicles face the risk of destruction. Such disadvantages are reduced to a large
extent, if the illumination task is performed by a small-sized unmanned aerial
vehicle.Manufacturedaccording to”Stealth” technology, thevehicle is difficult
to detect and kill. The problem is to execute its control in such a manner so
that the vehicle would be able to fulfil the task of target illumination with
sufficient accuracy.

On the modern battlefield, light small-sized UAVs perform the mission of
ground target detection, tracking and illumination. Their modified versions,
combat UAVs, are supposed not only to autonomously detect the target, but
also destroy it with on-deck infrared homingmissiles (tests on the combatmo-
del of Israeli Pioneer [1]). Alternatively, equipped with a warhead, they per-
form homing function in accordance with a specified homing algorithm (e.g.
American vehicle called Lark [9]). The present paper puts forward a control
algorithm for such combatUAVs,which onhaving autonomously detected tar-
gets, attack them (e.g. radar stations, combat vehicles or tanks) or illuminate
themwith a laser (Fig.1).

Figure 2 presents the diagramof geometrical relationships holdingbetween
the kinematics of motion, in respect one to another, centres of mass of UAV
and the target (points S, C) andpoint G (intersection of target detection and



The dynamic model of a combat target... 553

Fig. 1. General view of combat UAVmission performance

Fig. 2. Kinematics of combat UAV target homing guidance



554 Z. Koruba, E. Ładyżyńska-Kozdraś

observation line – LTSOwith the Earth surface). On the basis of this diagram
and following figures (Figs.2-6), there kinematical equations of motion for
UAV, LTSO, point G and the target were derived.

2. UAV navigation kinematics

2.1. Kinematic equation of UAV motion

Kinematics of UAV reciprocal motion and the ground target with the ad-
opted co-ordinate systems shown in Fig.2.

Projections of the left and the right hand of equation (2.3)1 on the axes of
the system O0xesyeszes yield the following system of equations

dRes

dt
=V s[cos(ϕ

s
χ−χs)cosϕ

s
γ cosγs+sinϕ

s
γ sinγs]

dϕsχ

dt
Rescosϕ

s
γ =−V s sin(ϕ

s
χ−χs)cosγs (2.1)

dϕsγ

dt
Res =V s[cos(ϕ

s
χ−χs)sinϕ

s
γ cosγs− cosϕ

s
γ sinγs]

where Res is radius vectors centre ofmass ofUAV, V s – vector ofUAVflight,
ϕsγ,ϕ

s
χ – angles of inclination anddeflection of vector Res, γs, χs –UAVflight

angles and desired UAV flight angles.

The equations above showmotion of the point S (UAV centre of mass) in
relation to the motionless point O0 (the origin of the terrestrial co-ordinate
system). The path ofUAVmotion in the terrestrial co-ordinate systemwill be
described by the following equations

xsx0 = Rescosϕ
s
γ cosϕ

s
χ ysx0 = Rescosϕ

s
γ sinϕ

s
χ

(2.2)
zsz0 =−Res sinϕ

s
γ

2.2. The equation of motion of target detection and observation line
(TDOL)

A procedure similar to that adopted for kinematic equations of UAV mo-
tion will give the following LTSO equation of motion

dξN

dt
= Π(t0, tw)(Vsxn−Vgxn)+ [Π(tw, ts)+Π(ts, tk)](Vsxn−Vcxn)



The dynamic model of a combat target... 555

−
dχn

dt
ξN cosγn = Π(t0, tw)(Vsyn−Vgyn)+ [Π(tw, ts)+Π(ts, tk)](Vsyn−Vcyn)

(2.3)
dγn

dt
ξN = Π(t0, tw)(Vszn−Vgzn)+ [Π(tw, ts)+Π(ts, tk)](Vszn−Vczn)

where ξN is the distance frompoint G or C to S, γn,χn – angles of LTSO in-
clination and deflection, respectively, Π(·) – functions of rectangular impulse,
t0, tw, ts – instant of start of area penetration, target detection and start of
target tracking and illumination, respectively, tk – instant of target tracking
completion (mission completion).
Components of thevelocity vectors V S,VG and VC in the relative system

Sxnynzn take the following form

Vsxn = Vs[cos(χn−χs)cosγncosγs− sinγn sinγs]

Vsyn =−Vs sin(χn−χs)cosγs

Vszn = Vs[cos(χn−χs)sinγncosγs− cosγn sinγs]

Vgxn = Vg[cos(χn−χg)cosγncosγg − sinγn sinγg]

Vgyn =−Vg sin(χn−χg)cosγg (2.4)

Vgzn = Vg[cos(χn−χg)sinγncosγg− cosγn sinγg]

Vcxn = Vc[cos(χn−χc)cosγncosγc− sinγn sinγc]

Vcyn =−Vc sin(χn−χc)cosγc

Vczn = Vc[cos(χn−χc)sinγncosγc− cosγn sinγc]

where γg,χg; γc,χc – angles of inclination and deflection of velocity vector in
point G and of target velocity vector.
Trajectory of point G

dReg

dt
= Π(t0, tw)Vg cos(ϕg −χg) xgx0 = Reg cosϕg

dϕg

dt
= Π(t0, tw)Vg sin(ϕg −χg) ygy0 = Reg sinϕg

(2.5)

Kinematcs of target motion

dRec

dt
= Vc[cos(ϕ

c
χ−χc)cosϕ

c
γ cosγc+sinϕ

c
γ sinγc]

dϕcχ

dt
Reccosϕ

c
γ =−Vc sin(ϕ

c
χ−χs)cosγc (2.6)

dϕcγ

dt
Rec =Vc[cos(ϕ

c
χ−χc)sinϕ

c
γ cosγc− cosϕ

c
γ sinγc]



556 Z. Koruba, E. Ładyżyńska-Kozdraś

The target trajectory in the terrestrial co-ordinate system is described by the
following equations

xcx0 = Reccosϕ
c
γ cosϕ

c
χ ysx0 = Reccosϕ

c
γ sinϕ

c
χ

(2.7)
zsz0 =−Rec sinϕ

c
γ

where ϕcγ, ϕ
c
χ are angles of inclination and deflection of vectors Rec.

3. Determination of desired UAV flight angles

The UAV flight angles χs and γs in the seeking phase and during attack on
the detected target will be determined from the following relationship

χ∗s = Π(t0, tw)χ
p
s+Π(tw, tk)χ

n
s γ

∗

s = Π(t0, tw)γ
p
s +Π(tw, tk)γ

n
s (3.1)

Those above are distribution equations due to the functions of rectangular
impulse Π(·), which occur in them. Thus they offer an option to describe
changes in the UAV flight angles at its different stages.

The UAV flight angles χs and γs in the seeking, transition to tracking
phase and laser illumination of the detected target have the following form

χ∗s = Π(t0, tw)χ
p
s +Π(tw, ts)χ

t
s+Π(ts, tk)χ

o
s

(3.2)
γ∗s = Π(t0, tw)γ

p
s +Π(tw, ts)γ

t
s+Π(ts, tk)γ

o
s

where γos, χ
o
s are UAV flight angles in target tracking and laser illumination,

γts, χ
t
s – UAV flight angles in transition from programmed flight to target

tracking flight.

Quantities χps and γ
p
s stand for pre-programmedUAV flight angles in the

phase of the Earth surface patrolling (target seeking), therefore they are pre-
set time functions

χps = χ
p
s(t) γ

p
s = γ

p
s(t) (3.3)

Prior to the determination of UAVflight angles χos and γ
o
s, an assumption

is made for the instance of seeking and simultaneous laser illumination of the
detected target (Koruba, 2001).

For the sake of simplification, let us assume thatUAVmotion, both during
the penetration and tracking, takes place in a horizontal plane at the pre-set



The dynamic model of a combat target... 557

altitude Hs, whereas the target and point G move in the terrestrial plane.
Then, we will be able to assume that

γos =0 γc =0 γg =0 (3.4)

Furthermore, for the sake of convenience, a notation is introduced

rN = ξN cosγn (3.5)

and the time derivative of this expression calculated

drN

dt
=
dξN

dt
cosγn− ξN

dγn

dt
sinγn (3.6)

Taking into account (3.4)-(3.6), we can limit further considerations to pla-
nar motion in the horizontal plane and after inserting (3.4)-(3.6), equations
(2.5) have the form

drN

dt
= Π(t0, tw)[Vscos(χn−χ

p
s)−Vg cos(χn−χg)]+

+Π(tw, ts)[Vscos(χn−χ
t
s)−Vccos(χn−χc)]+

Π(ts, tk)[Vs cos(χn−χ
s
s)−Vccos(χn−χc)]

(3.7)
dχn

dt
= Π(t0, tw)

Vs sin(χn−χg)−Vg sin(χn−χ
p
s)

rN
+

+Π(tw, ts)
Vs sin(χn−χc)−Vc sin(χn−χ

t
s)

rN
+

+Π(ts, tk)
Vs sin(χn−χc)−Vc sin(χn−χ

s
s)

rN

Wecanmake ademand that at the instant of target detection,UAVshould
automatically start target tracking flight, which consists in the vehiclemotion
at the pre-set distance from the target rN0 = ξN0cosγn = const (in the
horizontal plane at the constant altitude Hs).
Until the distance rN between points S and C is different from rN0, the

program for the angle deflection χs = χ
t
s and γs = γ

t
s, is determined from

(Koruba, 1999)

dχts
dt
= aχ sgn(rN0−rN)

dχn

dt
γts =0 (3.8)

which makes UAV either approach or move away from the target (depen-
ding on the sign of the function sgn(rN0 − rN)), in accordance with the



558 Z. Koruba, E. Ładyżyńska-Kozdraś

so-called proportional navigation method (Dubiel, 1980).When the condition
rN0 = rN, is satisfied, theprogramfor thecontrol of theangle χ

o
s is determined

from equation (3.7)1, which is rearranged to the form

Vscos(χn−χ
o
s)= Vccos(χn−χc) (3.9)

Hence, on the assumption that UAVmoves in the horizontal plane at the
constant altitude Hs, UAV flight angles in laser illumination of the detected
target χos and γ

o
s are determined from the relations

χos = χn−arccos
[Vc

Vs
cos(χn−χc)

]

γos =0 (3.10)

TheUAVflight angles duringattack on the detected target χns and γ
n
s , are

determined from the relations describing the proportional approach (Dubiel,
1980)

dχns
dt
= aχ

dχn

dt

dγns
dt
= aγ

dγn

dt
(3.11)

where aγ, aχ are coefficients of proportional navigation.

The above determined angles χ∗s and γ
∗
s specify the desired position in

space of the missile velocity vector. The discrepancy between the pre-set and
actual angular position of UAV velocity vector becomes the displacement er-
ror. It is also called an incongruence parameter for the autopilot automatic
regulation. The value and direction of the displacement error provides the ba-
sis to formacontrol signal,which after appropriate transformation is passed to
executive organs. They deflect control surfaces in the lateral and longitudinal
channel by the worked out angle values.

4. Combat UAV dynamics model

The description of UAV dynamics has been executed within the reference
system fixed to the object. The following physical model assumptions have
been adopted:

• UAV is treated as a rigid body with six degrees of freedom having mo-
vable but non-deformable steering modules,

• Vessel steering devices are weightless and their surfaces strictly control
aerodynamic forces andmoments,



The dynamic model of a combat target... 559

• UAV steering takes place with the application of three channels: recli-
nation through the sloping back of the height steering device as well as
through theprocess of tilting through theprocess of shuttlecock steering,

• UAVmasses and inertia moments are constant during flight,

• UAVpossesses OSxz symmetry surface – geometrical, inertial and aero-
dynamical.

Fig. 3. The system of forces andmoments affecting observation line during the flight

4.1. Dynamic equations of UAV motion

In the light of further analysis, description of UAV behaviour during spa-
tial flight will be developed on the basis of co-ordinates φs, θs, ψs and quasi-
velocites us, vs, ws, ps, qs, rs with the application of Boltzmann-Hamel equ-
ations, which are convenient for an object withmechanical settings connected
to it. These equations are generalised Lagrange equations of the II kind for
non-inertial settings described within quasi-co-ordinates. In the general form,
they are expressed as follows (Ładyżyńska-Kozdraś, 2004, 2008)

d

dt

∂T∗

∂ωµ
−
∂T∗

∂πµ
+
k
∑

r=1

k
∑

α=1

γrµα
∂T∗

∂ωr
ωα = Q

∗

µ (4.1)



560 Z. Koruba, E. Ładyżyńska-Kozdraś

where: α,µ,r = 1,2, . . . ,k; k is the the number of degrees of freedom,
ωµ – quasi-velocity, T

∗ – kinetic energy expressed in terms of quasi-velocities,
πµ – quasi-co-ordinates, Q

∗
µ – generalised forces, γ

r
αµ – three phaseBoltzmann

multipliers, determined from the following relation

γrαµ =
k
∑

δ=1

k
∑

λ=1

(∂arδ

∂qλ
−
∂arλ

∂qδ

)

bδµbλα (4.2)

The relations between quasi- and generalised velocities

ωδ =
k
∑

α=1

aδαq̇α q̇δ =
k
∑

µ=1

bδµωµ (4.3)

where q̇δ are generalised velocities, qk – generalised coefficients,
aδα = aδα(q1,q2, . . . ,qk) aswell as bδα = bδα(q1,q2, . . . ,qk) – coefficients which
are functions of the generalised coordinates. Simultaneously, the followingma-
trix expression [aδµ] = [bδµ]

−1 holds.

The researched UAV is described with the application of the following
coefficient vectors and generalised velocities

q= [q1,q2,q3,q4,q5,q6]
⊤ = [x0s,y0s,z0s,φs,θs,ψs]

⊤

(4.4)
q̇= [q̇1, q̇2, q̇3, q̇4, q̇5, q̇6]

⊤ = [ẋ0s, ẏ0s, ż0s, φ̇s, θ̇s, ψ̇s]
⊤

where x0,y0,z0 – location of UAV mass centre in terrestrial co-ordinate sys-
tem, θs, ψs, φs – angles of UAV longitudinal axis inclination, deflection and
tilt, respectively.

As well as quasi co-ordinates and quasi-velocities

π= [π1,π2,π3,π4,π5,π6]
⊤ = [πu,πv,πw,πp,πq,πr]

⊤

(4.5)
π̇= [ω1,ω2,ω3,ω4,ω5,ω6]

⊤ = [us,vs,ws,ps,qs,rs]
⊤

where us,vs,ws; ps,qs,rs] are components of vector of UAV flight linear ve-
locity and angular velocity.

Relationships between quasi- and generalised velocities are expressed as
(Ładyżyńska-Kozdraś, 2008)



The dynamic model of a combat target... 561







us
vs
ws






=















cosψscosθs sinψscosθs −sinθs
sinφscosψs sinθs+
−sinψs sinφs

sinφs sinψs sinθs+
+cosψscosφs

sinφscosθs

cosφscosψs sinθs+
+sinψs sinφs

cosφs sinψs sinθs+
−cosψs sinφs

cosφscosθs





















ẋ0s
ẏ0s
ż0s







(4.6)






ps
qs
rs






=







1 0 −sinθs
0 cosφs sinφscosθs
0 −sinφs cosφscosθs













φ̇s
θ̇s
ψ̇s







TheBoltzmann-Hamel equations, upon the calculation of Boltzmannmul-
tipliers as well determination of kinetic energy in terms of quasi-velocities,
yield the following differential equations of the second kindwhich describe the
behaviour of combatUAVupon the path during the process of target homing.

— Longitudinal motion

ms(u̇s+qsws−rsvs)−Sx(q
2
s+r

2
s)−Sy(ṙs−psqs)+Sz(q̇s+psrs)= X (4.7)

— Sidemotion

(4.8)ms(v̇s+rsus−psws)+Sx(ṙs+psqs)−Sy(p
2
s+r

2
s)−Sz(ṗs−qsrs)= Y (4.8)

—Lift

ms(ẇs+psvs−qsus)−Sx(q̇s+psrs)+Sy(ṗs+qsrs)−Sz(q
2
s +p

2
s)= Z (4.9)

—Tilt

Ixṗs− (Iy − Iz)qsrs−Ixy(q̇s−psrs)− Ixz(ṙs+psqs)− Iyz(q
2
s −r

2
s)+
(4.10)

+Sy(ẇs+psvs−qsus)+Sz(psws−rsus− v̇s)= L

—Reclination

Iyq̇s− (Iz − Ix)rsps−Ixy(ṗs+qsrs)− Iyz(ṙs−psqs)− Ixz(r
2
s −p

2
s)+
(4.11)

−Sx(ẇs+psvs−qsus)+Sz(u̇s−rsvs+qsws)=M

—Sloping away

Izṙs− (Ix− Iy)psqs− Iyz(q̇s+psrs)− Ixz(ṗs−rsqs)− Ixy(p
2
s −q

2
s)+
(4.12)

+Sx(v̇s−psws+rsus)−Sy(u̇s−rsvs+qsws)= N



562 Z. Koruba, E. Ładyżyńska-Kozdraś

The aforementioned set of equations upon the determination of component
forces X, Y , Z andmoments L, M, N, which have been generalised, consti-
tutes the general mathematic model of the described UAV dynamics. ms is
the mass of UAV, Ix, Iy, Iz – moments of inertia in relation to UAV indivi-
dual axes, Ixy, Iyz, Izx – moments of deviation of UAV, Sx, Sy, Sz – static
moments in relation to UAV individual axes.

4.2. Forces and external moments influencing UAV motion

The vector of forces and the moment of external forces exerting influence
upon the flyingUAV, the components of which constitute the right-hand sides
of equations of motion (4.7)-(4.12), constitutes the sum of the central influ-
ence, according to which the object moves. This vector is the resultant of the
following forces: aerodynamic Qa, gravitation Qg and steering forces (tilting
of aerodynamic steering devices) Qδ

Q∗ =Qa+Qg+Qδ =



















Xs
Ys
Zs
Ls
Ms
Ns



















=



















Xa

Y a

Za

La

Ma

Na



















+



















Xg

Y g

Zg

Lg

Mg

Ng



















+



















Xδ

Y δ

Zδ

Lδ

Mδ

Nδ



















(4.13)

Fig. 4. Gravity force as well as aerodynamic forces andmoments acting on UAV
during flight

Thematrix of external forces and gravity force (Fig.4)

Q
g = msg



















−sinθs
cosθs sinφs
cosθscosφs

0
−xccosθscosφs
xccosθs sinφs



















=



















Xg

Y g

Zg

Lg

Mg

Ng



















(4.14)



The dynamic model of a combat target... 563

Thematrices of forces and aerodynamicmoments (Fig.4) are of the follo-
wing form (Ładyżyńska-Kozdraś, 2004)

Fa =A







cosαscosβs cosαs sinβs −sinαs
−sinβs cosβs 0
sinαscosβs sinαs sinβs cosαs













Cx
Cy
Cz






+







Xqq

Ypp+Yrr
Zqq






=







Xa

Y a

Za







(4.15)

Ma =A







0 −za ya
za 0 −xa
−ya xa 0













cosαscosβs cosαs sinβs −sinαs
−sinβs cosβs 0
sinαscosβs sinαs sinβs cosαs













Cx
Cy
Cz






+

+A







cosαscosβs cosαs sinβs −sinαs
−sinβs cosβs 0
sinαscosβs sinαs sinβs cosαs













Cl
Cm
Cn






+







Lpp+Lrr
Mqq

Npp+Nrr






=







La

Ma

Na







where

A=
1

2
ρSV 2s

and ρ(Hs) is the air density at the given height Hs, S – the surface of referen-
ce (surface ofUAVwing), Cx,Cy,Cz –dimensionless aerodynamic coefficients
of components of aerodynamic forces: resistance, side and carrier force, respec-
tively, Cl, Cm, Cn – dimensionless aerodynamic coefficients of reclination, tilt
and slumpingawaymoments, respectively, and Xq,Yp,Yr,Zq,Lp,Lr,Mq,Np,
Nr are derivatives of components of the aerodynamic forces and their resect
to components of linear and angular speeds.

The location of the aerodynamic centre A with respect to the centre of
mass Os (Fig.4) is given by

rA = xai+yaj+zak (4.16)

UAV approach angle

αs =arctan
ws

us
(4.17)

and slide angle

βs =arcsin
vs

Vs
(4.18)

During the flight, UAV is steered with the application of an automatic
method.The process of steering takes place bymaking use of two tilt channels
through controlling the height steering system δH and the tilt of the steering
direction δV .



564 Z. Koruba, E. Ładyżyńska-Kozdraś

The matrix of forces and moments in the general method is presented as
follows

Q
δ =



















XδH XδV
0 YδV
ZδH 0
0 LδV

MδH 0
0 NδV



















[

δH
δV

]

=



















Xδ

Y δ

Zδ

Lδ

Mδ

Nδ



















(4.19)

Through the application of Boltzmann-Hamel method for the holonomic
constraints of UAV, equations of motion were determined. In the process of
substitution into equations (4.7)-(4.12) the stipulated forces and moments of
external forces actinguponUAV(4.13)-(4.19), thecompletemodelof dynamics
of UAV has been obtained.

4.3. UAV control

The control of UAVmotion is realised bymeans of deflections of ailerons,
rudder and elevator by angles δl, δm and δn, respectively.

The automatic pilot (AP) is responsible for UAVmaintaining the desired
flight path. On the basis of derived relations (3.1) and (3.2), it works out
control signals for the control executive system.

Having taken into account the dynamics of rudder and elevator deflections,
we arrive at the control formula for autopilot, which reads as follows

d2δm

dt2
+hms

dδm

dt
+kmsδm = km(γs−γ

∗

s)+hm
(dγs

dt
−
dγ∗s
dt

)

+ bmum
(4.20)

d2δn

dt2
+hns

dδn

dt
+knsδn = kn(χs−χ

∗

s)+hm
(dχs

dt
−
dχ∗s
dt

)

+ bnun

In the course of its mission, a light UAV can be affected by various kinds
of interference such as gusts of wind, vertical ascent and katabatic motion
of air-masses or shock waves produced by missiles explosions nearby. At the
instant of target detection, UAV automatically proceeds from the flight along
programmed trajectory to the target tracking flight in accordance with the
pre-set algorithm. In the case under consideration, the algorithm is meant to
maintain a constant distance from the target. This way, the most favourable
conditions for the target to bekeptwithin the view area of the tracking system
lens is provided. A sudden switch-over of the control system (from one flight
phase toanother)maydisturb theUAVmotion.Moreover, thedynamiceffects,
which result from the above-mentioned interference and control switch-over,



The dynamic model of a combat target... 565

change theflightquality andvehicle aerodynamic characteristics.Thecourseof
manoeuvres necessary to accomplish the assigned task suggests the occurrence
of clearly non-linear characteristics of the controlled object (Koruba, 2001). It
is therefore necessary to apply such an autopilot to UAV, so that the pre-set
accuracy of the programmed and tracking flight would be guaranteed, and at
the same time, UAV stability maintained.

5. Conclusions

TheUAVnavigation and control model presented in the paper fully describes
the autonomous motion of a combat vehicle whose task is not only to detect
and identify a ground target, but also to illuminate it with a laser or attack
it. The operator intervention in the UAV control process can be limited to
cases of total getting off of the pre-set path or target disappearance from the
view area of the tracking system lens (wind gusts, missiles explosions, etc.).
It is, therefore, necessary to providemeans of sending information about such
events to the control station so that the operator would be able to take over
the UAV flight control if the need arises. Further theoretical investigations,
calculations as well as simulation and experimental work should concentrate
on: a) determination of the optimum UAV flight program, b) the algorithm
for the Earth surface scanning to ensure the quickest target detection, c) the
program for the minimum time of UAV transition from the programmed to
target tracking flight or the detected target homing in accordance with the
pre-set algorithm.

Acknowledgement
This work was supported by PolishMinistry of Science and Higher Education –

project ON501003534.

References

1. Defence Procurement Analysis. Special Focus on UAVs, Summer 1998

2. Dubiel S., 1980,Rocket Construction. Part 1 – Overloads, edition 2,Warsaw
Military University of Technology Publishing House [in Polish]

3. Graffstein J.,KrawczykM.,Maryniak J., 1997,Modelling thedynamics
of automatically controlled unmanned aerial vehicle flight with the application



566 Z. Koruba, E. Ładyżyńska-Kozdraś

of non-holonomic constraints theory, Scientific Papers of the Chair of Applied
Mechanics, 4, XXXVI PTMTSSymposium ”Modelling inMechanics”, Gliwice
[in Polish]

4. Koruba Z., 1995, The options of terrain penetration and selected object trac-
king fromunmannedaerialvehicledeck,ScientificPapers ofRzeszówUniversity
of Technology, Mechanics, 45, 357-364 [in Polish]

5. Koruba Z., 1999, Unmanned aerial vehicle flight programme, ground surface
scanning and laser target illumination, Journal of Technical Physics, 4

6. Koruba Z., 2001, Dynamics and control of gyroscope on the deck of aerial
vehicle, Monographs, Studies, Dissertations No 25, Kielce University of Tech-
nology, pp. 285

7. Ładyżyńska-Kozdraś E., 2004, Modelowanie niesymetrycznego odpalenia
rakiety z manewrującego samolotu, Zeszyty Naukowe Katedry Mechaniki Sto-
sowanej Politechniki Śląskiej, Modelowanie w Mechanice, 23, 273-280

8. Ładyżyńska-Kozdraś E., 2008, Analiza dynamiki przestrzennego ruchu ra-
kiety sterowanej automatycznie, Mechanika w Lotnictwie, ML-XII 2008, Wy-
dawnictwo PTMTS,Warszawa

9. Unmanned Vehicles, 3, 3, August-September 1998

Dynamiczny model naprowadzania bojowego bezpilotowego aparatu
latającego

Streszczenie

Wpracyprzedstawionazostała koncepcja zastosowaniabezpilotowegoaparatu la-
tającego (BAL) do bezpośredniego rażenia celów naziemnych (stacje radiolokacyjne,
wozy bojowe czy też czołgi).Model kinematyczny ruchuBALuwzględnia poszczegól-
ne etapy realizowanej przez aparat misji, tj. lot programowy podczas wyszukiwania
celu, lot śledzący powykryciu celu oraz lot podczas samonaprowadzaniana cel. Przy-
toczono prawa sterowania dla pilota automatycznego bojowego BAL. Opracowany
został dynamiczny model ruchu automatycznie sterowanego BAL przy zastosowaniu
równań mechaniki analitycznej dla układów holonomicznych w układzie odniesienia
sztywno związanym z poruszającym się obiektem.

Manuscript received October 25, 2009; accepted for print December 3, 2009