Development and Design of the LandingGuidance and Control System for the S20

UAV

Joao Pedro Vasconcelos Fonseca da SilvaMechanical Engineering Department

Instituto Superior TecnicoAv. Rovisco Pais, 1049-001 Lisboa, Portugal

E-mail: joao.da.silva@ist.utl.pt

November 2014

Abstract – The work developed in this thesis fo-cuses on the design and validation of an autolandguidance and control system capable of landing theS20 UAV. To accomplish the task in hand, the sixdegree of freedom nonlinear model of the vehicleprovided by Spin.Works was studied, and the ac-tuators and sensors of the platform were modeled.The landing guidance strategy defines the threedimensional landing path using wind speed anddirection information and the desired landing sitegiven by the operator. The wind information is ob-tained from an Extended Kalman Filter EKF, thatestimates wind speed and direction using air speedand ground speed information provided by thepitot tube and the GPS respectively. Based on theassessment of the S20 UAV dynamics, the longi-tudinal control structure using a Linear QuadraticRegulator LQR and Proportional- Integral con-troller, was developed centered on controlling ver-tical speed, air speed and height. In order to im-plement the LQR, the model was linearized andsimplified to describe only the phugoid mode ofthe vehicle longitudinal motion. The lateral con-trol structure was provided by Spin.Works and isbased on path following algorithms. The final partof the thesis consists of performance and sensitiv-ity analyses of the landing procedure using MonteCarlo simulation techniques, where the variablesused were the wind speed and wind direction de-viation, and the initial position and heading of theaircraft.

Keywords – Fixed wing UAV, Autoland, LQR,EKF, Monte Carlo simulations.

1 Introduction

An Unmanned Aerial Vehicle (UAV) is an aircraft ca-pable of flying without an on-board human pilot. Itmay be remotely operated from a ground station, orby means of modern control systems, it may be au-tonomous in the sense that it is capable of fulfillingdifferent tasks without direct human interaction. Thedevelopment of UAV technologies has been recentlycentered on developing solutions for civil markets suchas agriculture, terrain mapping or fire surveillance.To fulfill these requirements, landing the UAV is oneof the key operations in flight which define the overallsuccess of the mission.Landing of UAVs has been a problem since the earlystages of their development. All weather and nightoperation of UAVs by manual controllers is extremelydifficult unless the reliance and load on the externalpilot is kept at a minimum. In order to overcomethese difficulties and expand the operational envelopeof the UAVs there has been a lot of research and de-velopment in the autolanding area.Following more traditional approaches, several con-trol techniques have been studied to land an UAV inpredetermined locations. Using robust control tech-niques in [1], the authors explored the possibility ofimplementing a control system where the H2 perfor-mance variables are responsible for controlling theaircraft states, such as speed and height, and theH∞ technique is implemented to minimize the atmo-spheric disturbances to the output. One other ap-proach was taken in [2] using dynamic inversion tech-niques. The underlying assumption of this study, con-sidering an accurate knowledge of the dynamic modelof the UAV, combined with the fact that the systemwas not tested for real wind conditions, leads one to

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conclude that this method is still to be proved. In[3] a different technique was adopted. This methodonly presents the control of the UAV in the longitu-dinal plane, based on independent control techniquesfor the elevator deflection command and thrust com-mand. Adaptive backstteping control techniques wereused for the elevator controller and the thrust con-troller is a PI structure. Finally in [4], a combinationof classical control techniques and first and second or-der pre-shape filters for input demands was used, withresults showing effective control of the trajectory andtouchdown point in the presence of wind.

2 Modeling the UAV motionand its components

In order to fully understand the S20 UAV characteris-tics and behavior, this section presents the S20 model,a small UAV developed in house by Spin.Works. It isa flying wing UAV and the philosophy behind the de-sign is to improve the ratio of maximum lift coefficientto minimum drag coefficient, thus improving energyconsumption and flight time. Table 1 summarizes theS20 specifications.

Total weight 2 kgPayload 0.4 KgWingspan 1.8 mEndurance 2 hRange 20 KmCruise speed 60 km/h

Table 1: S20 UAV specifications.

The sensors installed onboard the S20 are 3-axis ac-celerometers and gyroscopes, a 3-axis magnetometer,a GPS module and pressure sensors. In the scope ofthe autoland project, it is proposed the use of theSF10 Laser altimeter [5] to accurately measure alti-tude. The actuators installed are two servos, respon-sible for the actuation of the elavons, and an electricmotor that provides thrust.The existing sensors and actuators, along with theS20 UAV and the wind turbulence were modeled andimplemented in the simulator to accurately replicatethe dynamic behavior of the vehicle and its systems.Due to the fact that currently the laser altimeter isnot installed in the S20 UAV, it was not possible tostudy the behavior of the sensor. The solution for thisproblem consisted in assuming the worst case scenariopossibility, where after an estimation process to be im-plemented, the readings from the sensor would differ

±1 m from the mean height value. A model imposingthis solution was implemented.Once the complete model was implemented, the per-formance of the vehicle was assessed for trim glideflight. Trim flight conditions imply that the forces onthe aircraft are in balance and that the vehicle willremain in that particular trim condition until somedisturbance occurs. The trim glide flight test imposesthat the thrust input is null, δt = 0%, for which thevehicle stabilizes for a determined flight path angledepending on the trim speed. The vehicles trim wasperformed for a speed interval, V = [9, 18] m/s, andthe conditions summarized in table 2 were imposed.

State Variation State Variationµk 0 xg Naγk * yg Naχk 0 zg NaV Vt p 0αk * q 0βk 0 r 0

Table 2: Trim glide flight. No wind.

where ∗ indicates states that can freely vary until sta-bilization, Na stands for not applicable and applies tothe position states that vary without stabilizing. Theresults of the mentioned test were used to determinethe favorable conditions for the landing of the S20UAV, and are presented in figures 1 and 2.

8 10 12 14 16 18 2010

12

14

16

18

20

Velocity − V [m/s]

L/D

8 10 12 14 16 18 20−5

−4.5

−4

−3.5

−3

−2.5

Velocity − V [m/s]

gam

ma

º

Figure 1: Lift over drag and γt over trim velocity.

Described in figure 1 are two dependent variables, thelift over drag coefficient, L/D and the trim flight pathangle γt, varying over the trim speed and in figure2 is described the impact of the trim speed on thedistance covered over ground when the vehicle is de-

2

0 100 200 300 400 500 600 700 8000

5

10

15

20

25

30

35

40

Distance covared over groung [m]

z [

m]

FPA(V = 10[m/s])

FPA(V = 11[m/s])

FPA(V = 12[m/s])

FPA(V = 13[m/s])

FPA(V = 14[m/s])

FPA(V = 15[m/s])

FPA(V = 16[m/s])

00 500 600 700 8

Figure 2: Height over distance covered over groundover trim velocity.

scending from an height of z = 40 (m). From figure1 is possible to infer that the best gliding ratio oc-curs for a velocity of Vt = 12 (m/s) when L/D = 19and the flight path angle γt = −3 (deg). Relatingthe two figures, it is observable that the best glideratio, L/D = 19, corresponds to the flight trajectoryin yellow, that leads to the most distance traveledover ground. Due to the fact that the landing pro-cess has to be efficient, these flight path angle andspeed values should be avoided during descent, con-sidering that they lead to longer distances traveledover ground. One is looking for short and efficient de-scent trajectories. For this reason it was decided thatthe best descent flight path angle is in the intervalγd = [−3.5,−4] (deg) for conditions where the windis not present.

3 Landing guidance

The landing guidance strategy is responsible forguiding the vehicle from the time where the landingprocedures are activated until touchdown. Its corefunction is to receive data from the GPS and windestimator, and the desired lading site DLS inputfrom the operator and through imposed constraints,convert them into control references. By design, thelanding procedures always occur against the wind.To provide for an efficient landing, the strategywas divided into two: one responsible for guidingthe vehicle in the vertical plane, and the otherresponsible for guiding the vehicle in the horizontalplane. In order to evaluate the method proposed,and its limitations, Spin.Works defined the landingrequirements summarized in table 3.

Landing area 100 m × 30 mOperational wind speed ≤ 10 m/sWind direction 360 degTouchdown vertical speed ≤ 0.6 m/sTouchdown speed over ground ≤ 14.5 m/s

Table 3: Landing requirements.

3.1 Longitudinal guidance

The longitudinal guidance was designed to bring theS20 UAV from a determined altitude to the groundwithin pre-determined conditions. The procedure im-plemented considers three sequential flight phases:approach, descent and flare, as described in figure 3.

γd

Initial Position Buffer Point Descent Point

Flare Point

Touchdown

Wind

Horizontal

Ddfl

zfl

dd

zd

Approach Descent Flare

LP

Figure 3: Longitudinal guidance strategy.

The approach phase is used to bring the vehicle nearto the descent path. In this phase the air speed refer-ence is maintained at close to mission levels and thealtitude reference is maintained at values within therange of the laser altimeter:

Varef ' Vacruise (1)

zref < zaltlimit (2)

During the descent, the air speed reference is imposedas a constant and the height reference is determinedusing a function of position p = (N,E,D) and descentflight path angle γd:

Varef = Vad (3)

zref = tan γd × dc + zfl (4)

where zfl is the flare height and dc is the distancebetween the position of the vehicle at any given timeand the flare point, and is determined using:

dc =√

(Nfl −Nc)2 + (Efl − Ec)2 (5)

where (N,E)c are the coordinates of the vehicle atany given time and (N,E)fl are the coordinates ofthe flare point, both expressed in the ground frame.Due to the fact that the landing procedures will al-ways occur against the wind, the force that the wind

3

applies in the vehicle varies with the wind speed, andwith it the speed over ground of the aircraft. Withmore intense forces acting on the frame, the descentflight path angle can be increased without increasingthe speed over ground of the vehicle, hence reducingthe distance traveled over ground. The method im-plemented uses a descent angle increment related withwind speed:

γd = γ0 + Vwγinc (6)

Finally, the descent flight path angle when there is nowind is set to γ0 = −4 (deg) as proposed in section 2,and γinc is defined in section 5.The flare phase uses exponential equations dependenton time to shape the air speed reference:

Varef = (Va0 − Vatd)e−tτ2 + Vatd (7)

where Va0 is the air speed at the start of the flare,Vatd = 11 m/s is the targeted touchdown air speedand τ2 = 10s is the time constant at which the ref-erence air speed is decreased. And the vertical speedreference:

zref = (z0 − ztd)e−tτ1 + ztd (8)

where z0 is the vertical speed at the beginning of theflare, ztd = 0.3 m/s is the targeted vertical speedon touchdown and τ1 = 3.2s is the time constant atwhich the vertical speed is decreased.

3.2 Lateral guidance

The lateral guidance is responsible for guiding thevehicle in the horizontal plane defined by (N,E)G.Given wind direction, initial position and the DLS,the lateral guidance determines a set of waypointsthat define the horizontal path to be followed.

Initial position

Buffer point

Descent point

Flare point

Touchdown

dbf

dd

dfl

w

l

N

E

Figure 4: Lateral guidance strategy.

First the landing direction χL is defined using thewind direction χw:

χL = χw − 180 (9)

After the landing direction is defined the waypointsare calculated sequentially:

Ni+1 = Ni + sinχLdi+1 (10)

Ei+1 = Ei + cosχLdi+1 (11)

where the first waypoint to be defined is the flare pointand the following are calculated in the order describedin figure 4. di is the distance between the two way-points. The flare distance, dfl along with the bufferdistance, dbf are determined in section 5. As for thedescent distance, it is defined using the descent heightzd, the flare height zfl and the descent flight path an-gle:

dd = (zd − zfl) tan(γd) (12)

The output of the lateral guidance is the waypointsmatrix:

WP =

Nfl EflNd EdNbf Ebf

(13)

4 Wind estimation and control

The wind estimation tool is responsible for providingthe landing guidance with wind speed and directioninformation and the control platform is responsible forproviding the system with control commands in theform of elevator, aileron and thrust inputs. Figure 5is the sketch of their integration.

Pitot

GPS

Wind

Estimation

Approach

& Descent

Controller

Guidance

Longitudinal

Controller

zref

zaltimeter

L

DSL

Varef

zref

zref

z, Va

δe

δt

Lateral

Guidance and

Control

δa

WP

δe

Figure 5: Longitudinal guidance strategy.

The lateral guidance and control was designed andimplemented by Spin.Works and is not a topic of thiswork to improve it. The input of the entity is thewaypoints matrix defined by the landing guidance,and the purpose of the lateral guidance and controlsystem is to guide the vehicle through the landingplan defined prior, using aileron and elevator inputs,δa and δe. The rest of the entities is described in thefollowing sections.

4.1 Wind estimation

The estimation of wind speed and direction uses anExtended Kalman Filter EKF based on GPS and

4

Pitot tube measurements. The algorithm imple-mented follows [6], with the difference that the windis estimated in Cartesian coordinates, instead of Po-lar coordinates. The method used is based on findingthe wind vector ~Vw using the measured values of speedover ground ~V and air velocity ~Va:

~V = ~Va − ~Vw (14)

The speed over ground is given directly by the GPSand the air speed can be determined using the mea-sured pitot air speed Vp. Due to the fact that thepitot tube is mounted along the longitudinal axis ofthe vehicle, the measurement has to be corrected forinstallation errors as well as attitude variations. Thetwo are related using:

Va2 =

Vp2

cosαsenβ=q∞sf

(15)

where, α is the angle of attack, β is the side slip angle,q∞ is the dynamic pressure measured by the pitottube and sf is the scaling factor. With the groundspeed and air velocity defined, the equation combiningall three can be written:

(V N − VwN )2 + (V E − VwE)2 =q∞sf

(16)

The implementation of the EKF assumes that thewind is constant and horizontal. Additionally thepitot tube scaling factor sf is also estimated, com-pleting the state vector, x = [Vw

N VwE sf ]T . The

system dynamics are described as follows:

x(k + 1) = Fx(k) + ωk (17)

where

F =

1 0 00 1 00 0 1

, ωk ∼ N(0, Q) (18)

and the measurement equation h(x) is obtained from(16), and setting the measurement zk to be the dy-namic pressure q∞, the nonlinear observation systemis obtained:

zk = h(x)+vk = sf((V N−VwN )2+(V E−VwE)2)

)+vk(19)

By linearizing (19) and using the algorithm establishin [6] the EKF was obtained. The extended Kalmanfilter was tuned for the center of the wind speed land-ing envelop interval, Vw = 5 m/s, and table 5 sum-marizes the filters parameters.

The performance of the wind estimation tool is doc-umented in section 5.

Initial states

X0 =

3.83 m/s3.21 m/s

0.6125 kg/m3

Initial covariance

P0 =

0.282 0 00 0.282 00 0 0.0012

Measurement noise

R = 44(Pa2)

Process noise covariance

Q =

5e− 8 0 00 5e− 8 00 0 1e− 10

Table 4: Wind estimation. Kalman filter parameters.

4.2 Longitudinal controller

The longitudinal controller is responsible for the con-trol of the longitudinal motion of the aircraft. In [7]are described the two main modes of the longitudi-nal motion of an aircraft, the phugoid and the shortperiod. The S20 UAV is no exception and can be de-scribed in the same way. From the analyses executedto the linearized longitudinal motion of the vehicle itwas determined that the phugoid motion is the modeto be controlled because of the fact that it is slowerand less damped than the short period mode, hence itis the one determining the dynamic behavior of the ve-hicle. The approach taken to control the longitudinalmotion of the vehicle consisted in implementing an in-tegrative Linear Quadratic Regulator iLQR using thestates xilqr = [v z x1 x2]T , where v is the speedover ground, z is the vertical speed and (x1, x2) arethe integrative states of the first two. The lineariza-tion of the longitudinal motion of the vehicle leads toa state space representation of the system using thestates, x = [v α θ q]T , where θ is the pitch an-gle and q is the pitch rate. The next step consistedin trimming the system for V = 12 m/s, and per-form a set of state substitutions and approximationsto transform the original system, x into the desiredxilqr. Figure 6 documents the evolution of the systemthrough the process.

The transformations documented in figure 6 corre-spond to, first a substitution where θ is replaced forγ, using the relation:

γ = θ − α (20)

5

Figure 6: Phugoid mode varitation through the sim-plification process.

The second transformation is the longitudinal motionof the vehicle approximation using the phugoid mo-tion documented in [7], and the third step consistedof replacing γ with z using the trim speed:

z = γvt (21)

Finally, using Matlabs algorithm ”lqr2” the gain ma-trix K was obtained and by closing the control loop,the following eigenvalues were determined:

Eigenvalues-23.4-0.12-0.0046-0.013

Table 5: Closed loop eigenvalues. (xilqr = (A −BK)xilqr)

4.3 Approach and Descent controller

The approach and descent controller is responsible forthe height control during the respective phases. Themethod used to implement this entity consists in aProportional-Integral PI controller that actuates thesystem to neutralize the height error ez:

zref = ez[KPAD +KIAD

s] (22)

where KPAD and KIAD were found to be 0.4 and 0.5respectively.

5 Simulation setup and Results

5.1 Simulations description

The approach taken to assemble the simulation toolconsisted in merging the aircraft models, the land-ing guidance and the control structure described inthe previous sections into the same computational en-vironment, which for the present case was MatlabsSimulink platform. Figure 7 is the sketch of the simu-lation tool. The following sections present simulation

Wind

Estimation

Guidance UAVSIMControl Actuators SensorsX Yref cmd

^X

eDLS

Figure 7: Simulation tool.

results, for which the descent height and flare heightare fixed parameters: zd = 40 m and zfl = 6 m.

5.2 Landing guidance setup

In section 3 the landing guidance was presented, how-ever not all tuning parameters were determined. Inthis section the descent flight path angle incrementγinc, the flare distance dfl and the buffer distance dbfare defined using the simulation tool without any in-put uncertainties or perturbations.The first parameters to be defined are γinc and dbf .Simulations performed for the wind speed interval ofVw = [0 − 10] m/s showed that the relation betweenthe wind speed and the flare distance appears to bequadratic. Due to the fact that incrementing the de-scent flight path angle increases the air speed at whichthe vehicle is traveling, which in turn has an impactin the distance between the flare point and the touch-down, there is a specific γinc that linearizes the flaredistance over wind speed relation. The need to havea linear relation to the expression mentioned, comesfrom the fact that for safety reasons is desired to havea simple expression for the flare distance, so that theoperator can easily determine the safe area aroundthe DLS. Through simulations it was found thatγinc = 0.15 (deg sm ) linearizes the flare distance overwind speed relation, and at the same time reduces in20 m the descent distance for a wind speed of Vw = 10m. As for the flare distance, performing a linear re-gression to the variation of the flare distance over thewind speed the following expression was found:

dfl = 151.6− 5.9281Vw (23)

6

With (23) is finally possible to impose the DLS forwhich the landing guidance designs the trajectory ac-cordingly. Figure 8 shows the error imposed by thesimplifications imposed in terms of distance to theDLS.

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

1.2

1.4

Tou

chdo

wn

Err

or [m

]

Vw (m/s)

Figure 8: Landing error caused by the linear approx-imation of the flare distance.

To determine the buffer distance, several simulationswere performed under the worst possible conditionsin terms of flight trajectory convergence. It was im-posed a wind speed Vw = 0 m/s and a wind directionχw = 225 (deg), and an initial position and heading ofp = (−50,−50) m/s and χ = 225 (deg) respectively.For the DSL = (0, 0) m/s the vehicle flies with theinitial heading until the buffer point is reached andthen performs a 180 deg turn to align with the land-ing path. The exercise consisted in varying the bufferdistance until a satisfactory convergence between thelanding trajectory and the actual trajectory flown bythe vehicle was achieved. This principle guaranteesthe convergence under every wind conditions. Fromthe simulations it was determined that a satisfactoryconvergence occurs for dbf = 500 m.

5.3 Landing Simulation

This section presents a full simulation of the systemimplemented subjected to the initial parameters sum-marized in table 6.

The simulation process follows the same sequenceas the real mission. First, the wind is estimated,and once this process is complete the landing pro-cess starts. Figure 9 shows the estimated variablesfor the present simulation. Although the variablesare estimated in Cartesian coordinates, as explainedin section 4, they are presented here in polar coordi-

Position p0 = (100,−500)G mHeading χ0 = 180◦

speed V = 16 m/sWind speed Vw = 4 m/sWind azimuth χw = 225◦

DLS DSL = (0, 0)G m

Table 6: Initial simulation parameters.

nates for simplicity reasons.

0 50 100 150 200 250 3003.5

4

4.5

5

Time (s)

Win

d V

eloc

ity (

m/s

)

Wind speed. Error: 0.05 (m/s)Mean wind speed

0 50 100 150 200 250 30030

40

50

60

70

Time (s)

Win

d D

irect

ion

(º)

Wind direction. Error: 0.6 (º)Mean wind direction

Figure 9: Landing simulation: wind estimation re-sults.

The estimation results are presented in comparison tothe mean wind characteristics, and the errors in theprocess are small, εVw = 0.04 m/s and εχw = 0.7◦

which are encouraging results. Figure 10 representsthe desired landing trajectory and the actual trajec-tory flown by the vehicle.

−1000 −800 −600 −400 −200 0 200−900

−800

−700

−600

−500

−400

−300

−200

−100

0

100

E (m)

N (

m)

Mission PlanTrajectoryTouchdownGuidance points

LandingArea5

1

2

3

4

Figure 10: Landing simulation: horizontal trajectory.1 - Initial position, 2- buffer point, 3 - descent point,4 - flare point and 5 - DLS

Figure 11 documents the evolution of the control ref-erences and commands as well as the inputs of the the

7

frame.

0 50 100 150−1

0

1

2

zdot

(m

/s)

0 50 100 15010

15

20

Va

(m/s

)

0 50 100 150−5

0

5

de (

º)

0 50 100 1500

0.2

0.4

dt

Time (s)

Figure 11: Landing simulation: control references andcommands and system inputs. – Reference, – Com-mand, – Input.

Analyzing first the controllers performance is possi-ble to observe that the vertical speed control is muchmore efficient than the air speed control following thereference. Duo to the substantial dependency of bothvariables on the elevator inputs, it is difficult to ac-curately control them simultaneously. It was decidedto give priority to the vertical speed control which iscritical. From the input plots is possible to infer thatthe main actuator used during the descent and flarephases is the elevator. During those phases, the thrustinput presents a mean value of 4%. Figure 12 presentsthe evolution of the critical states during landing.

0 20 40 60 80 100 120 14010

15

20

(m/s

)

Ground speeedAir speed

0 20 40 60 80 100 120 140−10

−5

0

5

10

(deg

)

Flight path angleAngle of attackPitch

0 20 40 60 80 100 120 1400

20

40

(m)

Time (s)

Height

Figure 12: Landing simulation: States

In the first plot is possible to observe the variationof ground and air speed through the simulation. Therelation between the two allows us to infer that the

aircraft is first traveling down wind and at t = 50s ofthe simulation, the aircraft changes heading, turninginto the wind, traveling up wind, fact corroboratedby the trajectory described in figure 10. One can alsoidentify the three distinct phases of the longitudinallanding guidance, where the air speed is maintained,approach phase, until t = 90s the descent phase be-gins increasing the air speed, followed by a decreaseduring the flare phase. The second plot compoundsthe orientation information, namely the flight pathangle, angle of attack and pitch. The flight path angleis directly examined, as it has to respect the landingphases described in the speed image. Three variationsare observed, first the flight path angle is maintainedaround zero, and once the descent point is reached theflight path angle decreases. The values obtained hereagree with the expected descent flight path angle im-posed by the landing guidance, which means that thedescent path is being followed correctly. For a land-ing procedure under wind speed of Vw = 4 m/s theimposed descent flight path angle is γd = −4.6◦ andfrom the simulation values the variation obtained wasγd = [−4,−5.3]◦, hence the descent trajectory is be-ing correctly followed. In terms of pitch, is critical toverify that the touchdown occurs with positive pitchin order to minimize the impact. From the image ispossible to infer that the pitch on touchdown is closeto 5◦ which is considered acceptable. Finally, the lastimage shows the variation of height through the simu-lation, from which is possible to infer that the landingguidance phases correspond to the ones described inthe previous plots, and is also clear the difference inheight decrease between the descent phase and theflare phase.

5.4 Monte-Carlo simulation results

In order to validate and assess the performance of thedeveloped algorithms, 1400 Monte-Carlo simulationruns were performed. With the purpose of comparingresults, the desired landing site and wind directionwere fixed throughout the simulations, DLS = (0, 0)m and χw = 225◦. For each simulation the followingparameters were varied, randomly,

• The initial position could be any inside an areadefined by:[(−1725 ≤ (N0, E0) < 50)∩(−725 ≤ (N0, E0) < 50)

](m)

(24)

• 0 ≤ χ0 ≤ 360 (deg)

• 0 ≤ Vw,mean5 ≤ 10 (m/s)

• −25 ≤ ∆χw,mean0 ≤ 25 (deg)

8

where (N0, E0, χ0) is the vehicles set of initial posi-tion and heading which are uniformly distributed, Vwis the wind speed normally distributed, and ∆χw, alsonormally distributed, is the imposed wind deviationand accounts for the variation of wind direction afterthe wind is estimated onboard, hence the wind direc-tion after estimation at every simulation is defined asthe sum of the constant direction plus the variationafter estimation: χw + ∆χw. Figures 13 and 14 arethe representation of the 1400 simulation trajectoriesin the horizontal and vertical planes respectively.

−1500 −1000 −500 0−1800

−1600

−1400

−1200

−1000

−800

−600

−400

−200

0

E (m)

N (

m)

TrajectoryTouchdownLanding area

Figure 13: Horizontal plane trajectories.

−1800 −1600 −1400 −1200 −1000 −800 −600 −400 −200 00

5

10

15

20

25

30

35

40

45

50

Distance over ground (m)

Hei

ght (

m)

TrajectoryTouchdown

Figure 14: Vertical plane trajectories.

Figures 13 and 14 show that in spite of the significantdispersion of the initial position and heading, the pro-files converge to the landing approach profile, hencethe the mentioned have no influence in performance ofthe landing procedures. Figure 15 presents the windestimation errors.

0 0.2 0.4 0.60

100

200

300

400

500

600

700

Wind speed estimation error (m/s)

Num

ber

of c

ases

0 10 20 30 400

100

200

300

400

500

600

700

Wind direction estimation error (deg)

Figure 15: Wind estimation errors.

In terms of speed estimation, the results are encourag-ing due to the fact that the maximum error observedis 0, 5 m/s, and more than 50% of the estimationsare under the 0.1 m/s of error. On the other hand,the wind direction estimation presents very concen-trated error values in the interval [0◦ − 10◦] where99.5% of the results are, however, the other 0.5% aredispersed, being the worst case 42◦ of error in winddirection estimation. These results are the reason forthe seven landing trajectories outside of the main tra-jectory cone observed in figure 13. Finally, figure 16presents the touchdown coordinates for the set of sim-ulation runs.

Figure 16 shows that a single landing procedure faileddue to the fact it is outside the designated area. It wasalso determined that 96.1% of the landings are within30 m of the the DLS. As for the the other landingrequirements summarized in table 3, the speed overground presents few landings in the imposed limitof V = 14 m/s, the pitch is always inside the safelimits and the vertical speed presents a distributioncentered on 0.38 m/s with a maximum of 0.48 m/swhich is well inside the landing envelop. The land-ings with touchdown distances superior than 30 mwere studied in detail, as they are considered poorperformance procedures. From that exercise it wasconcluded that the performance of the system is en-hanced for medium to high wind speeds, and thaterrors in wind estimation and variations in the winddirection are an influence on the performance of the

9

−60 −40 −20 0 20 40 60−60

−40

−20

0

20

40

60

E (m)

N (

m)

TouchdownDLSLanding area

Figure 16: Touchdown coordinates.

landing procedures for the entire spectrum of windconditions.

6 Conclusions

The feasibility of using a guidance and control sys-tem based on position and speed commands for theS20 UAV landing was verified using 6-DOF nonlinearsimulations. Acceptable performance and robustnesswas demonstrated. The landing trajectory is definedbased on the wind direction and the DLS, because bydesign the trajectory is always against the wind. Si-multaneously, the wind speed is used to improve thedescent angle and flare distance, determined by thelanding guidance system. It was proved that thesecharacteristics generate more efficient landing results.The wind characteristics used in the landing guidancesystem are obtained using an Extended Kalman Fil-ter EKF, that estimates wind speed and direction.Simulation results showed that the EKF performedwell, although, it was also noted that the incorrectestimation of the variables can lead to poor landingperformances. The LQR was implemented using theapproximation of the aircrafts phugoid motion. Fromthe simulation results it was concluded that, becauseof the dependency between the two states, it was im-possible to accurately control one state without in-fluencing the other. It is then proposed to introducesome spoiler actuator to add drag into the system, orconventional flaps. The independent control of thesesurfaces will benefit the accuracy of the system im-plemented, by providing shorter landing trajectoriesand smaller touchdown speeds. Performance studiesprove that the designed guidance and control systemis flexible enough to cope with the complete S20 UAVlanding envelope, and at the same time achieve sat-

isfactory performance. These are important factorsthat lead one to conclude that system is ready to beimplemented and tested in the S20 UAV.

References

[1] Rui Wang, Zhou Zhou, Yanhang Shen, Flying-WingUAV Landing Control and Simulation Based on MixedH2/H∞. In Proceedings of the 2007 IEEE Interna-tional Conference on Mechatronics and Automation,August 2007.

[2] Shashiprakash Singh, Radhakant Padhi, AutomaticPath Planning and Control Design for AutonomousLanding of UAVs using Dynamic Inversion. In Amer-ican Control Conference, June 2009.

[3] Hann-Shing Ju, Ching-Chin Tsai, Glidepath Com-mand Generation and Tracking for Longitudinal Au-tolanding. In Proceedings of the 17th World CongressThe International Federation of Automatic Control,July 2008.

[4] P. Riseborough, Automatic Take-Off and LandingControl for Small UAVs. BAE Systems, Australia.

[5] SF10 Laser Altimeter, Product Manual - Revision 0.Lightware optoelectronics, 2014.

[6] Am Cho, Jihoon Kim, Sanghyo Lee, Changdon Kee,Wind Estimation and Airspeed Calibration using aUAV with a Single-Antenna GPS Receiver and PitotTube. In IEEE Transactions on Aerospace and Elec-tronics Systems, Vol. 47, No. 1 January 2011.

[7] Donald McLean. Automatic Flight Control Systems.Prentice Hall, 1990.

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