A study into relative navigation methods for automatic probe and drogue air-to-air refuelling

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A study into relative navigation methods for automatic probe and drogue air-to-air

refuelling

Jonas Samuelsson

Space Engineering, master's level 2020

Luleå University of Technology

Department of Computer Science, Electrical and Space Engineering

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Abstract

As the aerospace industry moves into more automatic systems and fully automatic systems the need for automatic air to air refuelling is be- coming essential to create an optimal aircraft system. It is not only needed for UAVs but also for piloted aircraft. For the aircraft to connect with the hose is a difficult procedure where a lot of things can go wrong. Creating an automatic system will remove any human error out of the procedure to create a more efficient refuelling procedure. This study is taking a look at relative navigation methods to connect the receiver aircraft with the hose in a probe and drogue refuelling system which can be used for an automatic aircraft system for refuelling.

To investigate different relative navigation methods a simulation environment was built using the relative position between each part of the system, the tanker, the hose, the drogue and the receiver. The system environment effects are also implemented to create an accurate environment that includes turbulence, wake effects, wind and bow wave effects.

The complexity of each part differs from each other. The two aircraft, tanker and receiver, are modelled in 1 and 3 degrees of freedom where the hose and drogue is modelled in 5 degrees of freedom to simulate the procedure. Using this simulation environment two different methods were tested, a straight on approach where the probe of aircraft aimed to always be aligned with the drogue and an offset approach where the receiver aimed to try to predict the movement of the drogue.

The findings from the simulation showed that analysing the bow wave effect on the drogue to then predict its movement by approaching with an offset was the most optimal approach. It allowed the receiver to do fewer movements during critical parts of the refuelling procedure and also were able to successfully dock during turbulent environment

I can conclude that using relative navigation that using a probe and drogue air to air refuelling an automatic system should be able to work.

The simulation can be expanded upon to create a more realistic environment that can give a more accurate representation of the real world dynamics. The aerodynamics of the aircraft need to be expanded upon and the aerodynamics of the disturbances can be more accurately implemented.

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Acknowledgements

I would like to thank my supervisors at SAAB Aeronautics, Fredrik Andersson and Joakim Bl˚ader, for the opportunity to write my master thesis at their department. Their support and guidance have been invalu- able throughout my work.

I would also like to thank my colleagues at SAAB who have been very welcoming, for our fun conversations during the 9AM coffee and the always fantastic Friday fika.

Finally i would like to thank my friends at Lule˚a University of Tech- nology for a time I will always treasure.

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1 Introduction

1.1 Background

On June 27, 1923 two de Havilland DH-4Bs in the U.S. Army Air service were able to connect via a hose so one of the aircraft were able to refuel the other and the first Air-to-air refuelling (AAR) was successful. Since then a number of endurance records have been achieved with the help of AAR methods. In 1949 the first non stop trip around the world was done after 94 hours of flight with a total of 4 AAR. The method is not only for setting endurance records, mid air refuelling is also a military advantage. AAR proved it self efficient during the cold war. First, during the Korean War when the closest American air bases to Korea were located in Japan and the range of the aircraft were not long enough so AAR were needed to carry out aerial missions over Korea. Later during the Cold War the United States devised a plan to always be ready to go to war with nuclear weapons. They planned to always have a nuclear bomber in the air to attack the Soviet Union if ever it was needed. For this to be efficient the bombers range needed to be extend and this was able to be done with AAR (Smith, 1998). The need for aerial refuelling has since the cold war been developed upon and more widely used. The technological advances in the field of unmanned aerial refuelling (UAV) have pushed the need for Automatic AAR without AAR capabilities the UAV are in a disadvantage compared to piloted planes.

There are two main ways of AAR, probe-and-drogue refuelling (PDR) and flying boom refuelling (FB). Both methods have their disadvantages and ad- vantages. Neither of the methods are flawless and therefore there is a need to understand the physics of the systems. The method discussed in this paper is PDR. The goal of understanding this system is to be able to create an automated AAR system for both unmanned aerial vehicles (UAV) and for piloted aircraft. Implementing an automated AAR system to a piloted aircraft will mean that the pilot need less training and also create a more efficient as well as safer for the pilots. The aerial refuelling manoeuvres are tricky and can lead to serious damages. It is also important for UAV to make them viable. Increasing the range for aircraft with the help of AAR is important in military operations which piloted aircraft still have an advantage in.

1.2 System Explanation and Scope

PDR is a refuelling method where retractable hose is attached underneath a aircraft or on its wings, referred to as the tanker, is to be connect to a refuelling aircraft, referred to as the receiver. The tanker is usually a large aircraft where up to three hoses can be deployed depending on the aircraft. On the end of each hose is a drogue similar in shape to a basket that have two uses, it helps the docking as it creates a larger target and also creates favourable aerodynamics for the system (Fezans and Jann, 2018). To ensure successful AAR the procedures and equipment are standardised. This is shown in NATOs

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AAR refuelling guidelines. The hose varies in length between 15m to 27m. The refuelling procedure has a total of 10 stages as mentioned in Fezans and Jann, 2018.

1. Drogue inside the tanker aircraft 2. Drogue reeling out

3. Full trail, clear contact

4. Contact, but not in refuelling zone 5. In refuelling zone, fuel flow 6. In stand-off zone, fuel flow 7. In cut-off zone

8. Refuelling finished, disconnect 9. Separated

10. Drogue reeling in

The stages this report will cover is stage 3 and 4 of the refuelling procedure.

Stage 3 is when the receiver aircraft enter the area behind the tanker to start approach the drogue and stage 4 starts when the probe has made contact to with the drogue. In these two stages an automatic refuelling system need to accurately determine the relative position between the drogue and probe on the receiver for a successful refuelling. To achieve an automatic docking the sensors to estimate the position can only have an error of around ten centimetres (Mati et al., 2006). Reaching these error margins, a vision based navigation can be used to determine the relative position. Approaching the hose to fast can result in a hose whip effect. This whip effect discussed in Haitao et al., 2014 occurs when there is slack in the hose during when the receiver successfully docks with the drogue. The aerodynamic forces acting on the slack hose creates a whip like a effect that can lead to disastrous consequences, damaging hose, drogue and/or receiver. The faster the receiver approaches the hose the greater the whip effect will be. To reduce this effect the hose reels in during the connection which allows the receiver to dock at a larger relative velocity. Even with this system implemented the relative velocity is still important to control. When the probe connects with the drogue successfully and the hose is reeled in to stretch the hose before the refuelling starts. The fuel flow from the hose ranges from 870 kg/min to 3650 kg/min with a total pressure of maximum 3.5 bars (NATO, 1981). The fuel probe on the receiver is placed differently depending on aircraft type for an example SAAB Gripen has the probe behind the cockpit on the wing and the F-35 have their probe halfway across the nose. The aerodynamic forces will therefore be different. When the receiver come close to the drogue the bow wave of the receiver pushes the drogue away from the the aircraft. It is therefore important to model the bow wave of each aircraft type so the dynamics of the drogue can be estimated. Knowing the movement of the drogue the aircraft can approach with an offset and as the bow wave hits the drogue the probe and drogue can be perfectly aligned. This is how the pilots are trained for piloted AAR.

The goal of this paper is to create a relative navigation algorithm for PDR AAR by creating a simulation of the system. There has been little research

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done into relative navigation algorithms to successfully connect with the probe automatically. However, there has been a lot of research done into each part of the PDR system with a goal to achieve an automatic PDR AAR, the key references for each part is used to create a simulation of the system to achieve the goal. Two different aircraft models will be modelled in the system for different bow wave effects. SAAB Gripen that have the probe mounted behind the cockpit and the F-16 which have the probe mounted in front of the cockpit.

This is done to see if different navigation algorithms is needed for different aircraft models. Using different aircraft types the results can then be applied to different UAV models to determine the optimal relative navigation algorithm.

The dimensions of the aircraft used in this paper is not a real representation of the two aircraft. The models are named after the two aircraft where the inspiration came from. The simulation will also be done at different altitudes and with different hose length to see if this will impact the navigation algorithms.

To reach this goal the following steps are done:

– Create a simulation model.

• A simple dynamic model of the tanker and receiver.

• Dynamic model of the hose and the drogue.

– Determine a relative navigation algorithm to estimate relative position to the drogue.

– Create a simple control algorithm for the tanking procedure.

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2 Method

2.1 Aerodynamic forces

To model the movement of the system we first have to understand the aerodynamic forces acting on the system. The aerodynamic forces are directly related to velocity of the wind

F = 1

2ρSCV². (1)

Here ρ is the atmospheric density, S is the reference area, C is the aerodynamic coefficient and V is the total wind velocity. To explain the aerodynamic forces acting on the system the changing variable of the force equation is the wind.

Determined through different wind components. The wind components on the two aircraft are

Vtanker = V_∞+ Vatm (2)

V_reciever = V_∞+V_vortex+ V_atm+ V_drogue. (3) V_∞ is the free stream velocity, V_vortex represent the vortexes created by the tanker, V_atm represent the wind, turbulence as well as wind gusts that can oc- cur and finally V_drogue is the velocity components around the drogue. This component is small and can be neglected. The hose is only affected by the atmosphere, the free stream and the tanker vortexes during the tanking procedure Vhose= V_∞+ Vvortex+ Vatm. (4) Finally, the aerodynamic forces acting on the drogue during flight are the wind components coming from the tanker, the free stream, the atmosphere and the bow wave from the receiver

Vdrogue= V∞+ Vvortex+ Vatm+ Vbow. (5) V_bow is the bow wave from the receiver when the aircraft come close to the drogue. The bow wave is dependent on the form of the body of the receiver and where the probe is attached (Dai et al., 2016). The movement of the hose and drogue system is very dependent on which aircraft is refuelling. An automatic refuelling approach would be quite different from aircraft to aircraft as the effect of the bow wave only occurs when the drogue is close to the aircraft. The bow wave has very little effect, if not zero, on the hose because the hose do not reach far over the bow of the receiver.

2.2 Reference Frames

To create a functioning system and be able determine the position of the probe relative the drogue a reference system needs to be created.

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Figure 1: Coordinate System in the east direction behind the receiver

Figure 2: Coordinate System in the north direction behind the receiver During the simulation OT is the origin of the system. The variable pdrogueis the position of the drogue relative the tanker. During the simulation the coordinate system of the receiver, probe and the drogue is aligned with the tanker. In order for a successful refuelling the distance between the probe and the drogue, prel, is estimated.

prel = [xrel, r] r = yrel+ zrel (6) when xrel = 0 and krk < rT (where rT is the target radius) the docking is successful. These two variables is also used to determine the different navigation algorithm explained in a later section. The position of the receiver and probe relative the tanker, p_reciever is also important know when the receiver moves

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when it approaches the drogue. The tanker, if not said otherwise, is assumed to fly at a constant altitude and velocity.

2.3 System dynamics

To create the simulation model MATLAB , MATLAB SIMULINK and MAT- LAB Simscape is used to determine the motion of the system.

2.3.1 Aircraft dynamics

The aircraft movement around a body fixed axis reference frame can be explained with six equations for the 6 degrees of freedom (DOF)

m( ˙U + qW − rV ) = X − mgsin(θ) + T cos(θ) m( ˙V + rU − pW ) = Y − mgcos(θ)sin(φ)

m( ˙W + pV − qV ) = Z − mgcos(θ)cos(φ) + T sin(θ)

Ixp + I˙ xz˙r + (Iz− Iy)qr + Ixzqp =L Iyq + (I˙ z− Iy)pr + Ixz(r²− p²) =M I_z˙r + I_xzp + (I˙ _y− Ix)qp + I_xzqr =N.

The first three equations is the translation equations of motion and the last are the rotational equations of motion. The dynamics for the two aircraft in the simulation are simplified because the dynamics of the 6-DOF freedom creates a very complex control system (Etkin, 1972). This is not needed to achieve the goal of this paper. The aircraft dynamics simplified and modelled in only 3-DOF with only the translation considered. To control the movement of the probe relative the drogue the simplified equations of motions of the receiver are established to move the in y and z direction to align the probe with the drogue in the y-z plane show in figure 2. In the y-direction the equation is simplified to

m_Ry¨_R= T_yR−1

2C_dyRρS_Ry˙_R² (7)

T_yR represent the change in lift to act in the y_R direction, this in reality can be a rotation about the x axis of the body for an example. C_dyR is the drag coefficient in the y direction and m_Ris the mass of the receiver. The sum of all the forces acting in the aircraft in the z_R direction is

m_R¨z_R= 1

2C_LRρS_RV²− mRg (8)

V is the tanker velocity, m is the mass of the receiver and g is the gravity. Any drag forces in the z-direction is neglected as they are very small due to the

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velocity in the z-direction is small. To control the height the control variable is the change in the lift coefficient which is manipulated with the help of elevators (Bryson, 1994)

CL= CLR(α) + CLRδδeR (9)

where C_LR(α) is the initial lift coefficient, C_LRδ is the change in lift coefficient from a change in elevator angle, δ_eR. Equation 9 in 8 gives

mR¨zR= 1

2(CLR(α) + CLRδδeR)ρSRV²− mg (10) using Taylor Approximation to linearise equation 7 around a velocity in the y direction, ˙yR, of 0m/s and homogenise equation 10 give

m_Ry¨_R= T_yR (11)

m_Rz¨_R=1

2C_LRδρS_RV²δ_eR. (12) With these two equation a simple controller is created align the probe and the drogue. When the probe and drogue is aligned the receiver need to be able to move in the x-direction as show in figure 2. In the x_R-direction the relative velocity is controlled. This is because to dock the probe with the drogue the receiver needs to be moving at a faster velocity than the tanker. However the receiver can not move to fast and not to slow. Moving to fast can cause the hose whip effect which can can have disastrous consequences and moving to slow will not result in a successful docking. The force equation in x-direction is similar to equation 7

mRx¨R= TxR−1

2CdxρS ˙x²_R (13)

where T_xR is the force from the engine and C_dx is the aerodynamic coefficient in x direction. Using Taylor approximation to linearise equation (13) around the tanker velocity, V, and homogenise it gives the following

mRx¨R= TxR− CdxRρSRV ˙xR, (14)

this equation is then used to control the relative velocity of the receiver. The tanker is considered to fly steady at a constant velocity however due to the unsteady nature of the aircraft, the tanker can move along the zT direction, equation (8)

mTz¨T =1

2CLTρSTV²− mTg. (15) The tanker is controlled in the same way as the receiver by changing the lift coefficient as in equation 9 giving the equation

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mT¨zT = 1

2CLT δρSTV²δeT (16)

after homogenising. Here the subscript T represents the tanker. Movement in y direction is not considered in the simulation as it is assumed to be negligible.

The tanker is a assumed to be large and a steady aircraft. So if there are any effects from the disturbances it would most likely be in the z direction.

2.3.2 Hose and Drogue Dynamics

To model the hose and drogue dynamics the hose is modelled as a series of lumped masses as shown in Ro et al., 2009.

Figure 3: Illustration of hose joints and links to describe the hose dynamics The lumped mass, mk, connected with mass less links lk and lk−1 where k ∈ {1, 2, 3, ..., N }. N is the total number of lumped masses in the system. The mass of the link is distributed to adjacent lumped mass. The mass of a lumped mass is the sum of half the mass of upper link, lk, and half the mass of the lower link, lk+1. Each lumped mass represents a joint in the system. The mass of the drogue is added to the last lumped mass which is only half the mass the upper link, l_N, and the mass of the drogue. To simulate this model it is then constructed in Simulink using the Simscape toolbox.

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Figure 4: Hose model with 8 links and 8 lumped masses.

Figure 4 shows the implementation of the theory in Ro et al., 2009 is implemented into simulink when N = 8. Each lumped mass has a joint connected to it with a rotational degree of freedom around the z-axis and the y-axis. The hose can move in all direction in the xyz-plane. Rotation around the x-axis is not considered because any rotation around that axis has no effect during the tanking procedure. The forces acting on the system is distributed on each lumped mass

Qk= mkg +1

2(Fk+ Fk+1) (17)

where Qk is the sum of all external forces acting on on the lumped mass, Fk

and Fk+1 is the aerodynamic force acting on the adjacent links. Finally g is the gravity vector in the positive z-direction, figure 2. The aerodynamic force acting on each link depend on the orientation of each link

Fk =1 2ρ

(Vhose• nk)²πdklkct+ +kVhose− (Vhose• nk)nkk²dklkcn

Vhose− (Vhose• nk)nk

kV_hose− (V_hose• n_k)n_kk

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the first term in equation (18) is the tangential force acting on the hose segment and the second is the normal force. nk is the direction of which each link is oriented in the reference frame, lk is the length of each link, dk is the diameter of the hose, ct and cn are the tangential and normal aerodynamic coefficient respectively. These values are determined experimentally and taken from Ro et al., 2009. The forces acting on the last lump is different because the aerodynamic forces on the drogue is added

QN = (mN + md)g + 1

2FN + FD (19)

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Fd is the aerodynamic force acting on the drogue. The force acting on the drogue is determined in a similar manner

F_D= 1

2ρ(V_drogue• Vdrogue)(πr²_D

2 )C_D V_drogue

kVdroguek (20)

r_D is the radius of the drogue and C_D is the aerodynamic coefficient of the drogue. This equation assumes that the drogue is always parallel to the x-axis in the reference frame. The aerodynamic coefficient of the drogue can vary from around 0.5 to 1.1 depending on the drogue model (Ro et al., 2007).

Table 1: Hose and Drogue Data Drogue coefficient, C_d 0.8 Drogue mass, md 30kg Drogue radius, r_d 40cm Normal coefficient, cn 0.21 tangential coefficient, c_t 0.001 Hose diameter, d 5cm

2.3.3 Tanker Movement interactions

Due to the wind not always being homogeneous the tanker will most likely move when there is a wind gust or entering a turbulent area.

2.4 Modeling of Wind Disturbances

The wind disturbances Vvortex, Vbow and Vatm are modelled. V∞ is constant in the simulation. To simplify the aircraft dynamics the disturbance will only affect the aircraft in the upward-downward direction in figure 2.

2.4.1 V_vortex

The wake wind velocity the tanker aircraft can be modelled with the horseshoe model as shown in Lewis and Blake, 2008. Their research shows for an aircraft that travel close behind an aircraft that the aircraft is affected by side wash and little up wash and down wash. This agrees with the modelling done in Ro et al., 2009. To model the effect of the wake disturbance the tanker is considered to be moving straight with a constant forward velocity. So the wake velocity will then be constant in all direction with small noise added. The hose is assumed to be attached on the wing of the tanker for the simulation.

2.4.2 V_atm

The atmospheric wind can be divided into three sources the steady wind, gusts and turbulence. The assumption done in the simulation is that the tanker will

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travel in the wind direction. In the Aerodynamic block set which is included in Simulink there are blocks that are able to model the three sources. The steady wind is considered to be zero in the simulation since there is not a large change in the direction of the system and therefore the effect of the steady wind does not change. The navigation algorithm will be tested both during turbulence and non-turbulence conditions. The block used to simulate the turbulence is

”Dryden Wind Turbulence Model” and a wind gust block is also added as a disturbance.

2.4.3 V_bow

The bow wave effect is very important to understand as it is one of the largest disturbances during a PDR AAR that is often the cause for an unsuccessful refuelling (Zhai et al., 2019). A lot of research and simulation have been done on the bow wave effect during AAR. Most of the available research have been done on the F-16 aircraft. The magnitude of disturbance changes over the body of the receiver as shown in Dai et al., 2016 the effect also attenuates quickly as the distance from the body increases (Zhai et al., 2019). V_bow can be divided in to sources from where the wind is coming from as shown in Zhai et al., 2019

Vbow= Vnose+ Vcockpit+ Vwings+ Vprobe+ Vother. (21) If we take a look at the Gripen aircraft the probe is behind the cockpit. The disturbance need to be modelled into sections as the initial disturbance is only from the nose. Vnose but as the drogue come closer to the probe, effects from other sources are added and the effect from the nose disappears. So the disturbance can be represented into sections that depend on the position of the drogue (Dai et al., 2016). Creating an accurate aerodynamic simulation of the bow wave is outside of the scope of this article. This report only uses an ap- proximate model of the bow wave effect to be able to determine an effective navigation algorithm for a safe and efficient docking. The two sections that will be modeled for simplicity and available research is V_noseand V_cockpit. Using the result from Dai et al., 2016,Wei et al., 2016 and Zhai et al., 2019. It is clear that the effect of the bow wave is acting mostly upward and in the north direction.

There is some side wash around the cockpit and at the tip of the nose but as it attenuates quickly the effect is small. A simplified model of the bow wave

Vbow= Vnose+ Vcockpit (22)

and the components is modeled as a linear function as the drogue approaches the probe

Vnose= ∆Vnosexrel+ Vnose0, xrel∈ [xn1, xn2] (23) V_cockpit= ∆V_cockpitx_rel+ V_cockpit0, x_rel∈ [x_c1, x_c2]. (24)

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Here the ∆Vnose, Vnose0,Vcockpit and Vcockpit0 are the constants explaining the linear function of the change in wind velocity from the. xrel is the position from the probe to the drogue. Lastly, [xn1, xn2] [xc1, xc2] distance from the probe where there is an effect from each section as can be shown in figure 5.

Figure 5: Bow of the receiver with the two sections (cockpit and nose) The profile of the wind velocity around the bow of the two aircraft bodies is shown in figure 6.

Figure 6: Shows the bow velocity around the two aircraft bodies. The distance is from the probe to where the bow wave effect starts.

The probe on the Gripen body is placed further back than it is compared to the F-16. It is important to note that this is not a real estimation of the bow wave. The assumption is done as the bow wave comes closer to the probe there is a larger body that will then result in a larger bow wave velocity. The values are estimated from the results found in Dai et al., 2016,Wei et al., 2016 and Zhai et al., 2019. Using these two velocity profiles different navigation methods

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can be tested and see if any can be potential start point to design an automatic AAR.

2.5 Control and Navigation

The target the receiver is aiming for has a radius of 40 cm but to successfully dock the area is half that. In the simulation the position of the receiver relative the drogue is assumed to be perfect. The velocity of the receiver need to be high enough so the probe just does not push the drogue but actually connects but not to large that to cause the hose whip effect. The desired relative velocity should be higher than 0.5 m/s and not less than 0.2m/s. To dock the receiver aircraft with the drogue a closed loop PID-controller is used inside a closed feedback loop to move the aircraft. PID-controller is chosen because the different plants are independent and it is a very robust and easy tool to use. PID stands for proportional plus integral plus derivative. The control is a closed feedback loop.

Figure 7: Implementation of the PID controller

Figure 7 shows how the feedback loop is constructed. G(s) is the equation of motion discussed in section 2.3.1. The input, R(s), is the distance between the probe and the drogue. The signal is then fed into the PID-controller, D(s). The equation for the PID controller is

D(s) = kp+kI

s + kds (25)

where k_p, k_i, k_d is the proportional gain, integral gain and derivative gain respectively. The proportional gain is related to the system error. Increasing the proportional gain reduces the error but increases the oscillation of the system.

The integral control minimises the steady-state tracking error as well as minimises the steady-state output response. The integral gain works then to reduce the error that the proportional feedback gives the system. Lastly the derivative gain is changed to increase the system stability, speeding up the transient response and reducing the overshoot. Combining the three gains into the closed loop system as shown in equation (25) the system can be easily designed (Gene F. Franklin, 2015). Simulink have a block implemented that makes the design

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of the PID very easy, called PID, which is used in the Simulink design. It is assumed that the control loops are independent of each other. As PID only works for a single input and single output (SISO) system. So a separate PID-controller is implemented and tuned for each equation of motion discussed in section 2.3.1.

H(s) is the sensor noise which in the simulation is non existent as the sensor is considered to be perfect, so it has no effect on the control loop. W(s) is any outside disturbances that the two aircraft are affected by, which have been discussed in section 2.4. Disturbance into the system is only modelled in the z-direction on the tanker and receiver.

The ways the receiver can approach the drogue is limited. The body of the receiver is not allowed to collide with the drogue. The goal of the docking should both be safe and efficient. First step to design an optimal control system is to determine the area where the drogue is in danger of colliding with the receiver or where the effect of the bow wave is not favourable.

Figure 8: Displaying the area where the drogue should be positioned during the procedure

In figure 8 the view is from behind the aircraft where the probe is located to the side of the cockpit on aircraft like it is for Gripen. The idea is the same of the probe would be located on the nose. The red dashed area is the area where the drogue should no be located. If the drogue passes the in to the red zone the aircraft should pull away from the drogue so the aircraft and drogue is at no risk of colliding. When initialising the approach the receiver should have the drogue on the same side of the aircraft as the probe. It is assumed that the position relative probe and the drogue is from the probe to the centre of the drogue, the radius of the drogue must then be accounted for determining the two areas. The distance from the probe and the aircraft is Prel is the distance from the probe to the origin of the drogue. To describe the relative navigation approach to the drogue, it can be divided up into 3 different phases, figure (9).

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Figure 9: Different navigation areas during aerial refuelling procedure.

For an optimal refuelling procedure the phase are determined by the different disturbances the system is occurring as well as the control and navigation mea- sures that are needed. Phase 1 the disturbance on the hose and drogue is only from the atmosphere, the vortexes from the tanker and from and the free stream.

In this phase the initial approach angle can be determined and set to minimise movement in phase 2. In phase 2 the drogue is over the body of the aircraft.

During this stage the bow wave disturbance is also affecting the drogue and the receiver should fly steady with as little movement as possible to avoid collision.

In phase 3 it is important that the receiver is travelling at the correct relative velocity to ensure a successful docking. Two different ways of navigating to the drogue will be discussed. The first is the straight on approach, where the receiver always has its probe aligned in the yz-plane with drogue throughout approach, r = 0. Where the importance of the control lies in the relative velocity between the tanker and the receiver. The second is an offset approach. In phase one the receiver will approach the drogue with an offset r 6= 0. The offset must be estimated from simulation and test. The offset depend on system velocity, elevation, hose characteristics, drogue characteristics and receiver model. The goal of this approach is to move as little as possible in r and to maintain a steady relative velocity.

2.5.1 Straight on method

If we take a look at the straight on approach where the relative velocity is controlled. What determines the velocity is then the distance x and the distance krk, where krk can be seen as a threshold that changes with the distance x. If outside this threshold the velocity should either be zero or the aircraft should breakaway and start over.

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Figure 10: Shows two different navigation approaches for straight on method The velocity can be expressed as shown in figure 10. As the drogue is further away from the receiver the threshold can be larger so the receiver adjusts its position to be aligned with the drogue and at the same time move closer the drogue. The drogue movement shown in Dai et al., 2016 shows that as the drogue enters the bow wave the drogue moves away from the receiver. So if the drogue is above the receiver when the drogue enters the bow wave it gets pushed away from the receiver so there is no threat of any collisions. If the relative velocity at this point is too high the receiver do not have the time to adjust its position in time to dock. With this docking method all three variables of the receiver are being changed frequently during the docking to maintain its position behind the drogue.

2.5.2 Offset approach

The other approach where the goal here is maintain the same relative velocity during the docking and the only change the position in y direction and z direction. The receiver moves toward the drogue with an offset that predicts the movement of the hose. This way it can hopefully travel with a higher relative velocity than the straight on approach, as the drogue moves into position and not the receiver. The offset is evaluated by testing the bow wave at different altitudes and hose length to see at what ranges the algorithm is viable. The off-

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set cannot be to large either so the drogue is underneath the receiver when the bow wave causing the drogue to be pushed down. This depend on the position of the probe shown in figure 8. Depending on how large the effect of the bow wave is there still needs to be manoeuvres in yz-plane as the offset cannot be large enough to compensate for the drogue movement inside the bow wave. The receiver, following the phases in figure 9, will in phase 1 adjust itself in the yz- plane at a relative offset position in p_rel. When entering the bow wave in phase 2 the drogue moves so the value of the offset in the control loop must change as x_rel decreases. The equation for the offset as x_rel decrease will be tested to try and find an optimal algorithm. First a linear relation and a quadratic relation, called case 1 and case 2 respectively

prel=axrel+ b (26)

prel=ap

(bxrel− h) + k. (27)

k is the distance from the probe when the drogue enters the bow wave, h is the initial offset value and the relative position in x direction is xrel∈ [xend, xstart].

The desired offset depend on the receiver. xstartis the relative position when the offset starts to decrease this value is when the drogue enters the bow wave. xend

is the relative position when the offset is set to zero. Simulating two different offset is to determine the importance of good modelling of the bow wave to be able to design a robust automatic refuelling procedure. An offset equation that reduces the movement of the receiver during the refuelling procedure creates a more optimal procedure.

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3 Results

3.1 Movement of hose effected by wind disturbances

To be able to determine any navigation algorithm the behaviour of the hose system must first be analysed under controlled disturbances to see how different disturbances and environmental conditions effect the system.

Figure 11: The effect from the bow wave on the hose from the two aircraft. 18 meter long hose at an altitude of 20km

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Figure 12: The effect from the bow wave on the hose from the two aircraft. 18 meter long hose at an altitude of 20km

Figure 12 and figure 11 shows the distance of the drogue relative the tanker.

The two graphs show the effect of the bow wave from the two bodies on the position of the drogue relative the tanker. First there is only the effect of the wake and the free stream that affect the hose and drogue as the drogue reaches a steady state. After a few seconds the drogue come into contact with the bow wave, the hose then stretches in the negative x direction in other words the displacement in z-direction decreases. The difference in effect of the two bodies is the change in the y-direction. For the Gripen body there is a a force acting in the y-direction that pushes the drogue away from the aircraft causing the position of the drogue in the x direction to have a small change in displacement shown in figure 11. Under the effect of the F-16 body when there is no force in the y-direction from the body the displacement in x direction is large as shown i figure 12. This means the the drogue comes closer to the probe when entering the bow wave causing the relative velocity between the drogue and the receiver to increase. If the velocity of the receiver is too large at this point the receiver may not have the time to adjust its position the probe may miss the drogue.

But in the case of the Gripen bow wave the aircraft needs to adjust its position in both y and z direction where it is only in the z-direction for the F-16. Taking a look at the effect on different altitudes which means different air density is also important to analyse. This is only done for the Gripen-body at an altitude of 5km where the density is 0.76 atm and at an altitude of 15km where the density is 0.19 atm.

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Figure 13: Hose movement to Bow wave disturbance. Hose length 18 m and at an altitude of 15km

Figure 14: Hose movement to Bow wave disturbance. Hose length 18 m and at an altitude of 5km

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The difference in movement of the hose at the two different altitudes the initial position of the hose is different. The difference in air density at these two altitudes is a factor of around 5. So any velocity change at an altitude of 5 km is 5 times stronger or weaker than at 15km as shown in equation 1. However as the drogue enters the bow wave, at t = 35s, the difference in the movement of the drogue relative the tanker is similar at two the altitudes shown in figure 13 and figure 14. The important data from these graphs is the change in drogue position as it enters the bow wave. The position before the bow wave is of no importance as it does not effect the relative position of the receiver to the drogue. As these two graphs the drogue behave similar when it enters the bow wave a standard navigation algorithm should be able to work between 5km and 15km. The length of the hose can also vary in the system from 15m to 25m so it is important to analyse its effect on the system as well. The simulation is done at the same altitude of 10km where the density is 0.41

Figure 15: Bow wave effect on a 15 meter long hose at an altitude 15km

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Figure 16: Bow wave effect on a 25 meter long hose at an altitude 15km As can be shown in figure 15 and figure 16 the initial position of the drogue is different due to the length of the hose in both x direction and in z-direction but identical in y direction. When the drogue enters the bow wave the change in position is similar for the two hose lengths. So in the span of 15m and 25m hose length a standard navigation algorithm can be determined. Then there is also the environment disturbance in the form of turbulence that can really causes an issue when performing the docking procedure. The test is done for a standard atmosphere at 10km at hose length of 18m.

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Figure 17: 18 meter long hose with a turbulent atmosphere at 15km As shown in figure 17 the drogue moves erratically in a turbulent environment as compared to 11. This movement makes it difficult for the successfully connect with the hose. It is necessary to design the system that is able to handle some turbulence so the navigation algorithms need to be tested during turbulence.

3.2 Straight on navigation method

The following simulations for navigating toward the drogue while the goal is to always be aligned with the drogue are done at an altitude of 10,000 meters and with a hose length of 18 meters. The receiver is positioned so that that the drogue is located in outside of the red area in figure 8. The red area starts at [yp, zp] = [0.5, 0.5], if the drogue passes these values the refuelling fails.

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Figure 18: Radial Position of the probe to the drogue and the threshold change rcone

Figure 19: Relative velocity of the receiver compared to the tanker using the conical approach

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Figure 20: Relative position of the probe to the drogue during the conical approach

Figure 21: Relative position of the receiver compared to the tanker during the conical approach

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Shown in figure 18 is the position of the probe relative the drogue in yz-plane.

If r < rT the docking is successful which it is in this case. rcone is the area of which the probe should be located in order for the receiver to move at a positive relative velocity to the tanker. During the tanking procedure the probe is always inside rconethe receiver is always moving at a positive relative velocity as is shown in figure 19 where the velocity zones correspond to figure 10. It is important to slow down the relative velocity as the probe came closer to the drogue. Otherwise the aircraft would move to fast and not have the time to adjust its position to successfully dock. It is important to note during this approach the drogue and probe is not aligned when entering the bow wave, at t ≈ 38s, resulting in a negative offset in the z-direction shown in figure 20.

So when the drogue enters the bow wave the drogue is pushed further in the negative direction so the aircraft needs to move further in the yz-plane in phase 2. Finally it is important to show how the aircraft moves in the system. The tanker is assumed to fly steady which is a good reference point for how the receiver and probe moves during the docking procedure, shown in figure 21. In order for the aircraft to remain aligned with the drogue the receiver need to due fast movements to follow the drogue as it moves when the drogue enters the bow wave to be able to hit the drogue. This requires precise movement with little overshoot and a good estimation of the drogue position relative the probe to not cause any problems during the approach. Testing the same approach but using the different threshold area in form of the cylinder in figure 10. This time the threshold is smaller initially to allow the aircraft to be more aligned with the probe in phase 1.

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Figure 22: Radial Position of the probe to the drogue and the threshold change rcylinder

Figure 23: Relative velocity of the receiver compared to the tanker using the cylider approach

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Figure 24: Relative position of the probe to the drogue during the cylinder approach

Figure 25: Relative position of the receiver compared to the tanker during the cylinder approach

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Here the threshold rcylinderis smaller to allow the aircraft to align the probe with the drogue shown in 22. As it is known that the bow wave pushes the drogue away from the receiver so the threshold can be increased initially in phase 2. Allowing the receiver to remain at a positive relative velocity. By limiting the relative velocity in phase 1 allows the probe to be better aligned with the drogue when entering phase 2. This in turn creates the opportunity for the aircraft to approach at a greater relative velocity in phase 2 and 3 show in figure 23. When being better aligned the receiver have to move less in the yz- plane shown in figure 25 compared to figure 21. Reducing the step also reduces the magnitude of the overshoot in phase 2 which is an advantage limiting the risk of any collisions with the receiver and the drogue. The downside of this algorithm is that the velocity changes in phase 1 as the condition of being inside the rcylinder threshold is met but due to the overshoot the receiver exits the threshold again, and velocity is set to 0 until the error is corrected.

3.3 Offset navigation method

The change in position as the drogue enters the bow wave, shown in figure 11, is determined to be a change of about 0.7 meters in y direction and 0.8 in the z direction. Theoretically the setting the aircraft with this offset would allow it to not do any manoeuvres during the approach. The drogue must then be closer during phase 1 as the drogue is pushed away from the aircraft. This is an issue in this case, the maximum distance the offset is 0.5 meters in both directions as show in figure 8. Setting the initial offset to 0.5 for both y and z direction in phase one. When entering phase 2 the offset must decrease as the drogue moves in the bow wave. The equation of the two cases are when xrel∈ [xend= 1, xstart= 5]:

Case 1:

zof f set=0.125xrel− 0.125

yof f set=0.125xrel− 0.125 (28)

Case2:

z_{of f set}=0.25p

(−x_rel+ 5) − 0.5 y_{of f set}=0.25p

(−x_rel+ 5) − 0.5

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Figure 26: Change in offset for the two cases inside the bow wave Figure 26 shows how the offset changes along the body of the receiver. The two cases of the Simulation are travelling toward the receiver with the same velocity shown in figure 27.

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Figure 27: Relative velocity of the receiver compared to the tanker during the offset approach

Figure 28: Relative position of the probe to the drogue during case 1 approach

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Figure 29: Relative position of the probe to the drogue during case 2 approach

Figure 30: Relative position of the receiver to the tanker during case 1 approach

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Figure 31: Relative position of the receiver to the tanker during case 2 approach Comparing the two cases phase 1 will then be the same as the offset is the same. The difference come when the the drogue hits the bow wave. Using case 1, the linear offset approach, the drogue is much closer to the aircraft for longer and also enters the capture region later as shown in figure 30 compared to case 2 in figure 29. When looking at the position of the receiver relative the tanker if figure 28 and figure 31 the graphs look nearly identical. Using both of these equations for the offset are viable as the drogue never are in threat of colliding with the receiver. There is still movement that have to be done in phase 2 and 3 using this method but there is less than the straight on method discussed in section 3.2.

3.4 Turbulence

The offset method clearly has an advantage over the straight on method. The receiver do not have to move as much when the drogue is over the body of the aircraft and the movement is also slower, which are both favourable for the procedure. Testing case 2 of the offset navigation algorithms and adding the turbulence shown in figure 17. Then also at the same time adding disturbances the tanker and the receiver which is also affected in the z-direction, making it harder for the receiver to navigate to the drogue and the tanker to keep a level flight. Using the same turbulence level as show in figure 17 is implemented on the whole system causes more problems than just a harder target to hit.

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Figure 32: Change in position of the tanker during high turbulence

Figure 33: Relative position of the receiver to the tanker during high turbulence

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Figure 34: Relative position of the probe to the drogue during high turbulence First off the position of the tanker starts to move in the z direction shown in figure 32 which translate more or less to the same movement to the hose. Then the receiver also gets the same disturbance while navigating toward the tanker.

It creates unstable movement in the z-direction that can be seen in figure 33. As the disturbance is only modelled in the z-direction for the aircraft movement in y-direction is smooth in comparison to z-direction. Even though there is a lot of turbulence the receiver is almost able to hit the drogue when xp= 0, zp= −0.22, figure 34. It is not within the defined capture distance of zp = 0.15 meters could still be inside the radius of the drogue. Even if it was able to hit the drogue the refuelling procedure should not take place at with this amount of turbulence.

It is also important to note that due to the disturbance the receiver does no reach its offset position before reaching the bow wave. Reducing the relative velocity in phase 1 allows the receiver to reach this point which is important for the procedure.

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Figure 35: Relative position of the receiver to the tanker during low turbulence When allowing the receiver to reach its offset position another problem arise.

The receiver will most likely collide with the drogue and as shown in figure 35, x_rel do not reach zero meaning the procedure is aborted. This means that the refuelling should not take place when there is this much turbulence. Lower- ing the disturbance to moderate the procedure is successful when allowing the receiver to reach the offset.

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Figure 36: Relative position of the receiver to the tanker during low turbulence ensuring the receiver reaches offset position

Figure 37: Relative position of the receiver to the tanker during low turbulence ensuring the receiver reaches offset position

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When xrelreaches zero the receiver is able to place the probe within the bound- aries set as shown in figure 36. To reach this there is still a lot of manoeuvring that have to be done to successfully dock, figure 37. The system is able to successfully dock with this amount of disturbance but it should not be recom- mended to refuel at this amount of disturbance either as the aircraft needs to do fast manoeuvres in order to successfully dock.

3.5 F-16

Using the same navigation algorithm as the previous section but now on the F-16 body with the bow wave shown in figure 6. Doing the same procedure as before. First by looking at how the drogue moves when entering the bow wave in figure 12 it can be determined that the movement is only in the z and x direction in this case. The drogue moves about 1.5 meters in the negative z-direction and 1 meter in the negative x-direction. This means that the drogue moves away from the receiver in the z-direction but closer in the x-direction. To compensate this movement an offset will be set in the z-direction of 1 meter and adding a light disturbance environment gives the result. It is important to note when the probe is located further forward on the aircraft than on the previous body.

Figure 38: Relative position of the probe to the drogue during the F-16 simulation

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Figure 39: Relative velocity of the receiver to the tanker during the F-16 simulation

Figure 40: Relative position of the receiver to the tanker during the F-16 simulation

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In order to successfully dock with the F16 with the same method the relative velocity is lower than then the Gripen case as the probe is further forward on the body, figure 39. If not the receiver was not able put the probe in alignment with the drogue fast enough. The receiver is able to reach the offset position before the drogue enters the bow wave, figure 38. The offset equation is not optimal either as the drogue receiver have to do some unnecessary movement that can be seen in figure 40. This means that the navigation methods needs to be unique for each aircraft in order to create a successful refuelling procedure.

This also shows that it is more optimal to approach the drogue that puts side force on the drogue. This reduces the relative velocity between the drogue and the probe giving the receiver more time to adjusts its position.

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4 Conclusion and Future Work

This study has looked at the PDR system as a whole. The movement of the hose has been analysed under controlled conditions when it comes into contact with the bow wave to establish relative navigation algorithms. The velocity relative the earth was constant through the study, 166m/s. Different hose length were tested and the change in position of the hose when the bow wave came into contact with the drogue the difference was insignificant. The same result was determined for the two altitudes. It was established that the relative navigation algorithms simulated were feasible for the hose length between 15 meters and 25 meter as well as for an altitude difference of 5km and 15km. Different navigation algorithms were tested at altitude of 10 km and with a hose length of 18 meters.

The test showed that approaching the drogue with an offset is the best way of navigating toward the receiver. The relative velocity can be higher and the receiver have to do smaller manoeuvres when the drogue is over the body of the aircraft to be able to connect the probe with the hose. This method also proved useful when adding disturbances to the system, even tough the drogue is closer to the body of the receiver it was never in danger of colliding with aircraft as the bow wave always pushes the drogue away from the aircraft. The simulation also proved that it is possible to successfully dock with the help of an offset during a turbulent environment when each part of the system were affected. The important step was for the receiver to reach its offset in phase 1 before entering the bow wave. As the turbulence has an affect on the receiver it takes longer for the aircraft to reach this point at the relative velocity needed to be decreased in phase 1. Using the same algorithm but for another body, in this case the F-16, did not prove to be as optimal and could be improved upon.

Approaching with an offset is still important but offset equation is in need of optimising. As the probe is also further forward the simulation showed that the relative velocity must be lower as the drogue enters the bow wave the drogue is dragged closer to the probe due to the bow wave, increasing the relative velocity between the probe and the drogue. This makes it difficult for the receiver to change its position in time for a successful connection.

To continue this study the two aircraft needs to be modelled to fit more into the real world. This would mean that a more complex aerodynamic environment around the probe need to be modelled for a better understanding of the system.

The wind coming from the wake of the tanker is considered to be uniform across the system which is not an accurate assumption of the system. Therefore creating a better vortex model can also be done to improve the simulation environment. More joints to the hose can also be added if there is enough computer power to handle the additional joints without the simulation crashing.

The model of the hose is as series of pendulums attached to each other which is a chaotic system any larger forces acting on the system makes it difficult for the computer to handle if the hose is made up of many joints. Looking in to different absolute velocity ranges can also be done with a deeper understanding of the aircraft aerodynamics and the aircraft parameters to find the optimal velocity range is also needed. From there creating an optimal control algorithm

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to follow the relative navigation algorithms discussed .

This study gives a start in to how relative navigation methods can be used to improve on automatic aerial refuelling. Here it is assumed that the exact position of the drogue relative the probe is known. However putting this in to practice is more difficult as there is no sensor that is perfect. The more perfect sensor generally means that is more expensive. To be able to use these methods four relative parameters needs to be known the position is of the probe relative the drogue in x, y and z direction as well as the relative velocity between the tanker and the receiver. The best navigation method using the offset approach allowed the control of the relative velocity to be less significant as the velocity could remain constant. Allowing the system to control less variables is more favourable for the system as a whole. However measuring these four variable accurately is still important for the relative navigation methods to be successful.

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A study into relative navigation methods for automatic probe and drogue air-to-air refuelling