This document discusses autonomous formation flight control for aerial refueling missions. It models the dynamics of a KC-130J tanker and F-16 receiver in close formation flight. A control strategy is designed using a rotating reference frame attached to the wingman aircraft. The strategy aims to control the wingman's position relative to the leader through state error feedback between the aircraft. Specifically, it controls the lateral and forward distance between the aircraft in the level flight plane, as well as the vertical distance. The control system design decomposes the problem into inner loop attitude control and outer loop trajectory control of the formation geometry.

1. 1 Introduction
Autonomous formation flight is currently an
important research area in aerospace community.
The aerodynamic benefits of formation and, in
particular, close formation flight, have been well
documented[1], [2]
. In earlier efforts[3]
, a leader-
wingman formation flight control problem was
investigated and a PID-type （ proportional integral
derivative） of formation controller was developed.
Ref. [4] describes the application of an “extreme
seeking” algorithm to the formation control problem.
In Ref. [5] a formation flight control scheme was
proposed based on the concept of Formation
Geometry Center, also known as Formation Virtual
Leader. Some of the initial experimental results of
formation flight were reported in Ref [6]. However,
in all the previous efforts, the formation control
problem is considered with the aircraft flying at
straight level flight conditions and/or under mild
maneuvering. In this work the formation control
strategy will be implemented in the case study of
aerial refueling racetrack mission. KC-130J tanker
and F-16 receiver configuration (Fig. 1) was used as
a case study in this paper.
Design of Fighter Flight Formation for Aerial Refueling Racetrack Mission
with Drogue-Hose Configuration
Ahmed Momtaz
Abstract: The flying of aircraft information necessitates the extension of the theory of
formation flight control to allow for three dimensional formation maneuvers. A leader and
wingman formation is considered. A rotating reference frame attached to the wingman is used
and special attention is given to the motion of the leader relative to the wingman. A thirteen
state, three inputs, and three disturbances signal control system which models the dynamics
of a two aircraft formation in three dimensional spaces is developed. The theory of formation
control was applied to KC-130J tanker and F-16 receiver configuration to study the
availability of performing such mission on a large scale. Three formation flight control
concepts are investigated. A proportional, integral, and derivative automatic control system to
maintain the wing aircraft in the specified formation geometry despite the leader’s maneuvers
is designed, and its performance is examined in simulation experiments. By adding special
compensation to each control law to maintain the design damping ratio and gain margin, it is
possible to reach the desired performance satisfying the predefined relative distances
boundaries.
Key words: autopilot; race track; formation control; compensator

2. Fig. 1 KC-130J tanker and F-16 receiver configuration
2 Receiving Aircraft Modeling
The F-16 nonlinear model has been constructed
using SIMULINK/ MATLAB. The plant requires
four controls, eighteen states, leading edge flap
deflection and a model flag as inputs as shown in
Table 1 and Table 2. Starting with calculating the
trimming points then performing the linearization
algorithms, the aircraft state space will be available
to calculate the optimal gain matrix that is required
for the formation controller design.
Table 1 F-16 aircraft states
State Passed to plant UNITS Passed from plant
used by plant
npos ft ft ft
epos ft ft ft
h ft ft ft
ф rad rad rad
θ rad rad rad
ψ rad rad rad
Vt ft/s ft/s ft/s
α rad deg rad
β rad deg rad
p rad/s rad/s rad/s
q rad/s rad/s rad/s
r rad/s rad/s rad/s
anx N/A g g
any N/A g g
anz N/A g g
M N/A - -
q N/A lb/ft2
lb/ft2
P N/A lb/ft2
lb/ft2

3. Table 2 Control inputs limitations
Control Input
UNITS
Used by nlplant
Min Max.
Thrust lbs. lbs. 1000 19000 lbs.
Elevator deg. deg. -25 25 deg.
Aileron deg. deg. -21.5 21.5 deg.
Rudder deg. deg. -30 30 deg.
Leading edge flap deg. deg. 0 25 deg.
Fig. 2 F-16 nonlinear modeling
3 Control Strategy
The formation control problem can be basically
classified as a Dynamic 3-D Target-Tracking
problem, where the objective is to track a certain
point (desired position) dynamically specified by the
leader. The main difference between conventional
‘trajectory-following’ flight and formation flight is
that in the first case the trajectory is typically pre-
defined and stored within the on-board computer
while in the second case the trajectory to be
followed is ‘produced’ on-line by the leader aircraft
flown under specific trajectory; thus, the trajectory
information has to be obtained in real time from
some of the relevant states of the leader aircraft
(position, velocity, etc.). Ideally, to achieve desirable
trajectory tracking performance, the formation flight
control strategy should be based on full state
tracking strategy. This concept can be concisely
expressed as
Wingman’s control inputs = Leader’s control
inputs + State error feedback
(1)
where the control inputs include deflections for the
throttle, elevator, aileron and rudder, while state
error feedback consists of the internal state variable
errors and trajectory state variable errors between
leader and wingman. Particularly, internal state
variable errors are angular rate errors and Euler
angle errors (pitch and bank angles); trajectory state
variable errors are, instead, given by projected 3-D
position and velocity errors (i.e., forward distance,
lateral distance and vertical distance, and their time
derivatives, as defined in next section). This
approach is based on the fact that, if the wingman
flies at the same position of the leader, a perfect
position tracking could be achieved under any
reasonable maneuvering the leader aircraft might
execute, since the leader and wingman aircraft are
sharing very similar dynamics (assuming same type
of aircraft). In reality, extra compensation might be
needed to account for the trajectory variable
difference between the leader and the ideal
wingman. This is because the desired wingman
position is shifted with respect to the leader’s

4. position. Since both the leader’s state and input
vectors are needed to calculate the wingman input, a
high communication bandwidth between the leader
and wingman is required. Among conventional
formation control schemes, the simplest scheme in
terms of the minimum amount of information from
leader is based upon an existing autopilot
(functioning as an “inner loop” controller) with an
additional “formation-autopilot” added on to an
“outer loop” controller. This outer loop controller
uses only trajectory measurements from the leader
available from GPS. Unfortunately, this simple
formation control scheme has shown desirable
performance only if the leader is flying at level
straight and/or performing mild maneuvers. A
reasonable tradeoff between the simplest and the
most complete schemes introduced above is given
by the use of Euler angles error feedback along with
trajectory error feedback by the wingman. The
control strategy discussed in this paper is based on
this approach.
3.1 Controller Design
Since formation control is a 3-D tracking
problem, the control task can be decomposed into
three sub-tasks: vertical distance (height) control,
lateral distance control, and forward distance
control. On the other hand, since the dynamics of the
aircraft attitude (angular movement) is much faster
than the trajectory dynamics (translational
movement), the whole dynamics exhibit a typical
two-time-scale feature. Therefore, the design of the
control system can be decomposed into two separate
phases, that is, the inner loop and the outer loop
design. The function of the inner loop controller is to
maintain and/or track the desired pitch/bank angle
command; the outer loop controller is based on the
designed inner loop controller and uses the desired
pitch/bank angle command as its output–tries to
maintain and/or track the desired formation flight.
3.1.1 Formation Geometry and Trajectory
Variables
As described above, formation flight control
problem can be decomposed as a level plane and a
vertical plane dynamic trajectory-tracking problem.
3.1.2 Level Plane Formation Definition
Fig. 3 shows the level plane formation
geometry. All the trajectory measurements, i.e.,
leader/ wingman position and velocity, are defined
with respect to a pre-defined Earth-Fixed Reference
x-o-y plane and are measured by the on-board
GPS’s. The pre-defined formation geometric
parameters are the forward clearance, fc, and the
lateral clearance, lc. The formation trajectory
variables in level plane, the forward distance, f, and
lateral distance, l, can be calculated from the
trajectory measurements and formation geometric
parameters as
( ) ( )
c
Lxy
FLLxFLLy
l
V
yyVxxV
l −
−−−
=
(2)
( )
c
Lxy
FLLxFLLy
f
V
xxVyyV
f −
−+−
=
)(
(3)
where 22
LyLxLxy VVV += is the projection of the
leader’s velocity onto X-Y plane. Accordingly, the
relative forward speed and relative lateral speed of
the wingman are defined as the time derivatives of
the forward distance and lateral distance
respectively, and are needed for formation control
purposes which can be calculated as
( )
Lx Fy Ly Fx
c L
Lxy
V V V V
l f f
V
Ω• •
−
= + + (4)
( )Lx Fx Ly Fy
Lxy c L
Lxy
V V V V
f V l l
V
Ω• •
+
= − − + (5)

5. There are basically two methods to obtain the
angular velocity (around the vertical axis) LΩ•
. One
method is to, first, calculate LΩ from the GPS
measurement ),( LyLx VV , then apply
conventional numerical derivative techniques to
estimate the time derivatives of LΩ ; within this
approach particular caution should be exercised due
to the sensitivity of the numerical derivative with
respect to measurement noise. A second approach
consists in using additional measurements from the
leader aircraft, that is using the following
kinematical relation (assuming 0=•
Lβ )
( sin cos ) / cosL L L L L L Lq rΩ Ψ φ φ• •
≅ = + Θ
(6)
The second approach requires not only the
vertical gyro (to measure bank angle Lφ and pitch
angle LΘ ) but also the angular rate gyros (to
measure pitch rate q and yaw rater) on the leader
aircraft. In this study the first approach was used
with the definitions provided above. The level plane
formation control problem can be subdivided into a
lateral distance control problem and a forward
distance control problem.
3.1.3 Vertical Plane Formation Definition
At nominal conditions, the leader and the wingman
aircraft are separated by a vertical clearance h. The
vertical distance, zδ , can then be calculated by
hzzz wL −−=δ
(7)
While its time derivative is given by
wzLz VVz −=•
δ
(8)
3.2 Control Laws
3.2.1 Lateral Distance Control
The objective of the lateral distance control is
to minimize the lateral distance l. The basic physical
principle of the lateral distance control can be
expressed by the following action-consequence logic
aileron rollrate bankangle lateral_speed lateral_distance→ → → →
In addition, the function of the rudder is to
augment the lateral-directional stability (by
increasing the Dutch Roll damping ). Therefore, the
lateral formation control law consists of an inner
loop controller controlling the bank angle and
augmenting the lateral-directional stability, and an
outer loop controller maintaining the predefined
flight formation with respect to the leader. The
control law, represented in Fig. 4, can be expressed
by:
Inner loop control law
)( gWWpAW KpK φφδ φ −+=
(9)
WrWR rK=δ
(10)
Outer loop control law
lKlK lldotLg ++= •
φφ (11)
3.2.2 Forward Distance Control

6. The objective of the forward distance control is
to minimize the forward distance f . This task can
only be accomplished through the involvement of
the throttle control channel. In fact, by
increasing/decreasing the throttle, the thrust of the
engine and then the speed of the aircraft is
increased/decreased; this, in turn, allows to control
the forward distance between leader and wingman.
The forward distance control law, represented in Fig. 5,
is given by
fKfK ffdotTT ++= •
0δδ (12)
3.2.3 Vertical Distance Control
The objective of the vertical distance control is
to minimize the vertical distance. This task is
accomplished through the use of the elevator control
channel. The vertical distance control law is similar
to the conventional altitude-hold autopilot with the
only difference being that the altitude reference may
vary according to the leader’s altitude. Similar to the
lateral distance controller, the vertical distance
control scheme can be designed using an inner loop
control scheme which is basically a pitch angle
controller and an outer loop controller which
provides an altitude control capabilities. This control
law is presented in Fig. 6.
Inner loop control law
)(0 gWWqEE KqK θθδδ θ −++= (13)
Outer loop control law
zKzK zzdotLg δδθθ ++= •
(14)
4 System Identification Process
In order to evaluate each branch in the
complete control system introducing reasonable
damping ratio, system identification process is
needed to evaluate the final response considering the
coupling between the different SISO(single input
single output) branches and the kinematics
nonlinearities.
4.1 Estimation of Simple Process Model
The System Identification allows to estimate
simple continuous-time process models
characterizing the static gain, dominating time
constants, and possible time delays (dead time).
They are the variants of the transfer function model
structure.
4.2 Initial Parameter Values and Parameter
Bounds
If no prior knowledge is available about the
parameters, a startup routine is invoked to come up
with initial parameter estimates. These are further
iterated to give the best possible model fit for the
data. Actually, in our process there is no initial guess
is provided and an automatic process is invoked to
estimate the initial values. If no qualified guess is
available, this is usually a better alternative than
entering an unstable value. However, if the
estimation process gives parameter values that seem

7. unreasonable, it might be worthwhile to try out
various initial guesses and upper and/or lower limits
of the parameters.
4.3 Compensator Design Using System
Identification Technique
A basic structure for lateral-directional control
model is presented in Fig. 4 that was used to
generate the linear model in order to compute the
optimum PID controller gains using (Adaptive
Genetic Algorithms with PI performance index
criteria ) and the compensator time constant through
the root locus tool so that achieving the desired
damping ratio through root locus tool. Phase lead
compensator structure will be as follows
1
1
c c
s z
G K
s p
+
= ×
+
(15)
The final design parameters for lateral-directional
control are given in Table 3. in the same manner it is
possible to calculate the design parameters for both
forward and vertical motions.
Table 3 Gain values with lead compensator parameters for lateral motion
Kp KΦ Kr Ki Kl KL KV Kq KӨ Kzdot Kz Z1 P1
.431 .29 .5 .425 .331 6.9 .98 .333 .123 .5 .8 .03 .313
5 Conclusion
The formation control law developed in
previous section was based on a linear aircraft
model. Such a controller, if properly designed, can
be guaranteed to perform nominally only when the
system is operating around the design point where
the linear model was derived from. However, non-
linear dynamic effects, particularly those associated
with the kinematics, cannot be ignored when the
aircraft is undergoing a significant trajectory
maneuver, i.e., flying at a large bank angle. Thus, it
is necessary that the designed controller be validated
through simulation using a nonlinear model so that
any major non-linearities in terms of trajectory
dynamics, such as non-linear reference
transformation and kinematical non-linearity, can be
accounted for. The non-linear aircraft model of
dynamics can be described by the following 6 DOF
equations plus kinematical equations. By applying
the scenario of the system identification technique it
is possible to reach the desired performance with a
reasonable damping ratio. The control strategy is
implemented by using SIMULINK. Fig. 7 shows the
nonlinear output response and the relative distances
in all directions that satisfy the predefined
boundaries according to the KC-130J specifications.
Fig. 8 shows the effect of adding compensation on
the damping ratio explained by root locus (SISO)
tool for lateral control branch through MATLAB
tool box. It is clear that the damping ratio has
reached a reasonable value (ζ=.5). Fig. 9 shows the
predefined trajectory of the tanker and the receiving
aircraft describing the plane relative distance for the
whole mission. It is clear from the Fig. 5 that the
maximum peak in the relative distances between the
receiver and the tanker usually become larger in the
transient points of switching the racetrack from and
to steady state flight after and before the steady
horizontal turn. Fig. 7 shows also that the
maximum relative distances between the tanker and
the receiving aircraft may reach over 50 (ft) in some
places of the racetrack trajectory, therefore it is
recommended to increase the radius of the tanker
horizontal turn over 25000 (ft) with bank angle
limit of 30 (deg) in case of performing racetrack
mission as shown in Fig. 9.
.

8. Fig. 3 Level plane formation geometry
Fig. 4 Lateral –directional control law
Fig. 5 Forward control law
Fig. 6 Vertical control law

9. Fig. 7 Nonlinear model output performance with compensation

10. Fig. 8 Root locus for lateral-directional control with and without phase lead compensator respectively
Fig. 9 Trajectory in x-y plane for both wingman and leader
References
[1] Meir Pachter, John J D’Azzo, Andrew W Proud. Tight
formation flight control[J]. Journal of Guidance,
Control, and Dynamics, 2001, 24(2): 246-254.
[2] Fabrizio Giulietti, Lorenzo Pollini, Mario Innocenti.
Autonomous formation flight[J]. IEEE Control Systems
Magazine, 2000, 20(6): 34-44.
[3] Meir Pachter, John J D’Azzo, Dargan J L. Automatic
formation flight control[J]. Journal of Guidance,
Control, and Dynamics, 1994, 17( 6):1380-1383.
[4] Paolo Binetti, Kartik B Ariyur, Miroslav Krstic, et al.
Control of formation flight via extremum seeking[A].
In: Proceedings of the America Control Conference[C].
[s.l]: [s.n.]2002. 2848-2853.
[5] Fabrizio Giulietti, Lorenzo Pollini, Mario Innocenti.
Formation flight control: a behavioral approach[R].
AIAA paper 2001-4239, 2001.
[6] Eugene Lavretsky. F/A-18 autonomous formation flight
control system design[R]. AIAA paper 2002-4757, 2002.
[7] Blake William, Dieter Multhopp. Design, performance,
and modeling considerations for close formation
flight[R]. AIAA paper 99-4343, 1999.
[8] Pachter M, Dargan J, D’Azzo J J. Automatic formation
flight control[J]. AIAA Journal of Guidance, Control
and Dynamics, 1994, 17( 6): 1380-1383.
[9] Pachter Meir, Andrew W Proud, D’Azzo J J. Close
Formation Flight Control [R]. AIAA paper No 99-4112,
1999.
Nomenclature

11. b Wingspan, ft Vy Projection of y velocity (east), ft/sec
c Mean aerodynamic chord, ft Vz Vertical velocity, ft/sec
f Forward distance, ft x Position on x-axis (north), ft
fc Pre-defined forward clearance, ft y Position on y-axis (east), ft
h Pre-defined vertical clearance, ft α Angle of attack, deg
l Lateral distance, ft β Angle of sideslip, deg
lc Pre-defined lateral clearance, ft θ Pitch angle, deg
m Aircraft weight, lb φ Bank angle, deg
p Roll rate, deg/sec ψ Heading angle, deg
q Pitch rate, deg/sec δA Aileron deflection, deg
q Dynamic pressure, lb/ft2
δE Elevator deflection, deg
r Yaw rate, deg/sec δR Rudder deflection, deg
S Wing platform area, ft2
δT Throttle command, lb
T Thrust, lb δz Vertical distance,
V Airspeed, ft/sec Ω Flight path angle in level plane, deg
Vx Projection of x velocity (north), ft/sec
Subscripts
L Leader
W Wingman
0 Trimmed condition