Aalborg Universitet

Adaptive Control System for Autonomous Helicopter Slung Load Operations

Bisgaard, Morten; la Cour-Harbo, Anders; Bendtsen, Jan Dimon

Published in:Control Engineering Practice

DOI (link to publication from Publisher):10.1016/j.conengprac.2010.01.017

Publication date:2010

Document VersionAccepted author manuscript, peer reviewed version

Link to publication from Aalborg University

Citation for published version (APA):Bisgaard, M., la Cour-Harbo, A., & Bendtsen, J. D. (2010). Adaptive Control System for Autonomous HelicopterSlung Load Operations. Control Engineering Practice, 18(7), 800-811.https://doi.org/10.1016/j.conengprac.2010.01.017

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Adaptive Control System for Autonomous Helicopter Slung Load Operations

Morten Bisgaard, Anders la Cour-Harbo, Jan Dimon Bendtsen

Department of Electronic Systems, Aalborg University, 9220 Aalborg East, Denmark, Fax:+45 98151739

Abstract

This paper presents design and verification of an estimationand control system for a helicopter slung load system. Theestimator provides position and velocity estimates of the slung load and is designed to augment existing navigation inautonomous helicopters. Sensor input is provided by a vision system on the helicopter that measures the position ofthe slung load. The controller is a combined feedforward andfeedback scheme for simultaneous avoidance of swingexcitation and active swing damping. Simulations and laboratory flight tests show the effectiveness of the combinedcontrol system, yielding significant load swing reduction compared to the baseline controller.

Key words: Helicopter control, Delay, Feedforward control, Kalman filters, Autonomous vehicles, Frequencyestimation

1. Introduction

A helicopter is a highly versatile aerial vehicle andits unique flying characteristics enable it to carry loadshanging in wires underneath the helicopter. Flying withan underslung load is known as either slung load or slingload flight and it is widely used for different kinds ofcargo transport. However, flying a slung load can bea very challenging and sometimes hazardous task as aslung load significantly alters the flight characteristicsof the helicopter. The pendulum-like behaviour of theslung load gives a high risk of pilot induced oscilla-tions that can result in dangerous situations (Hoh et al.[12]). Furthermore, unstable oscillations can occur athigh speeds due to the different aerodynamic shapes ofthe slung loads. There is therefore, from helicopter pi-lots and from the aerospace industry in general, a largeinterest in technologies that can address the challenge inoperating helicopter slung loads.

The focus of this research is on enabling slung loadflight in autonomous helicopters for general cargo trans-port. This is characterized by a suspension system thatuses a single attachment point on the helicopter and byunknown slung load parameters. Furthermore, for gen-eral cargo transport there is no specific tracking require-ment for the slung load, but stable flight must be en-sured.

The contribution of this paper is the development of acontrol system that can be integrated on autonomous he-licopters and thereby enable slung load flight for these.

This is achieved through a three-step approach: First aslung load estimator capable of estimating the length ofthe suspension system together with the system states,and thereby allowing the model to be adapted, is de-signed using vision-based sensor data. The second stepis the development of a feedforward control systembased on input shaping that can be put on an existing au-tonomous helicopter and make it capable of performingmanoeuvres with a slung load without inducing residualoscillations. The final and third step is to design a feed-back control system to actively dampen oscillations ofthe slung load. Both the feedforward and feedback aredesigned to easily handle varying wire length and to-gether with the adaptive slung load estimator they forman integrated control system as shown in figure 1. The

Helicoptercontroller Helicopter Slung load

controllerDelayed

estimatorSlungload

+

+ −

Helicopterstates

Slung loadstatesInput

shaperReference

Figure 1: Architectural overview of the swing damping controlscheme.

overall control concept is a classical cascaded schemewhere the outer loop controller (the delayed feedbackcontrol) generates references to the inner loop controller(the helicopter controller). Where a traditional externalreference input would be applied to the outer loop con-troller, it is here applied it to the inner loop. This means

Preprint submitted to Control Engineering Practice January 27, 2010

that the reference input is a desired helicopter trajectory.The control scheme presented here will only han-

dles the lateral and longitudinal modes and while this isthe primary influences Hoh et al. [12], the added slungload also affects the vertical helicopter dynamics. Thiswas analysed for a helicopter/ slung load mass ratio of0.07 to 0.43 in Bisgaard [5] and the conclusion was thatheave mode is almost unaffected by the slung load, butbecomes a little slower as the mass ratio rises. It will beassumed that the helicopter controller is capable of han-dling the small change of heave mode bandwidth andincludes an integration term that can handle the changein collective trim.

The paper starts with a review of previous work incontrol of helicopter slung load systems. Then the de-signs of the slung load state estimator, the feedforwardand feedback controller are given. Finally, the full con-trol scheme is verified through flight tests.

1.1. Previous WorkA number of different publications on control of heli-

copter slung load systems exist, but actual flight verifi-cation is very sparse in the literature. In Dukes [7] feed-back from the load velocity to either main rotor thrustangles or to attachment point position is analyzed. Itis concluded that feedback to rotor input gives only lim-ited performance while feedback to the attachment pointposition is more advantageous. The problem of state es-timation for slung load systems is mentioned in Dukes[8] and to overcome this problem an open loop controlapproach is suggested. This open loop control methodresembles input shaping in the sense that the controlleris designed such that excitation of the resonant modesis avoided, in this case by using appropriate spaced tri-angular pulses as control input. In Gupta and Bryson[11] an LQR controller is designed for a S-61 Sikorskyhelicopter for near hover stabilization with a single wiresuspension. SISO controllers are designed for the lateraland longitudinal axis taking wind disturbances into ac-count. The problem of acquiring reliable measurementsis discussed and it is suggested to use the angles of thesuspension cable as sensor input to a linear Kalman fil-ter. The resulting design is left untested, but stabilityand performance analysis shows satisfying results. Anactive control system mounted on the actual slung loadis proposed in Raz et al. [20]. It consists of two ver-tical aerodynamic control surfaces intended to dampenoscillation on the load yaw and lateral axis in a singlewire suspension system. Controller design is done us-ing LQR and it is shown through linear analysis that thesystem is capable of stabilizing the system up to quitehigh airspeeds.

Robust control is used in Faille and Weiden [10] forstabilization of a helicopter with a point mass slungload. Controller design is done based on a reduced or-der linear model usingH∞ synthesis and it is shownthrough simulation to be able to stabilize the sys-tem. Receding Horizon Optimal control is suggestedin Schierman et al. [23] and preliminary simulation re-sults are presented. A recent publication is Oh et al. [18]which looks at a helicopter carrying a cable suspendedrobot that is controlled through a number of adjustablelength cables. The nonlinear control design is done in-dependently for the helicopter and for the load systemand therefore relies on a controllable suspension system.

Twin lift system has also been the focus of someresearch through the past decades. In Rodriguez andAthans [22] a LQG control design is developed for atwin lift system with spreader bar and single load. Thecontroller uses a master/slave configuration of the he-licopters and simulations shows that the controller iscapable of stabilizing the system and tracking velocityreferences. Robust control on a similar system is alsoapplied in Reynolds and Rodriguez [21] whereH∞ isused and simulation is used to verify that the systemcan track velocity references. A feedback linearizationscheme is presented in Mittal et al. [17] where a twinlift system without spreader bar is considered. The con-troller is designed to adapt to an unknown slung loadmass and simulations is used to show that the system isstabilized by the controller.

For smaller scale helicopter the 1997 AUVSI In-ternational Aerial Robotics Competition showed au-tonomous flight with a slung load. The winning entryby Carnegie Mellon Miller et al. [16] demonstrated ob-ject collection by a controllable suspension system withPID controllers for helicopter and slung load system.Feedforward control was used to compensate for heli-copter motion in the slung load control, while the he-licopter controller was unaware of the slung load. Re-cently in Bernard et al. [4] autonomous helicopter slungload flight with both single and multiple small scale he-licopters was demonstrated where force feedback fromthe load attachment was used.

2. Slung Load State Estimator

The purpose of the estimator is to provide estimatesof the slung load states (χl ,

˙χl ∈ R3). It is designed

to augment an already existing inertial measurementunit (IMU) driven state estimator and it uses the esti-mated helicopter states (χh,

˙χh ∈ R3× S

3) as well as thebias and gravity corrected acceleration measurementsfrom the IMU (ah) as shown in figure 2. The estima-

2

Slung load Helicopterestimator

GPS

Compass

IMUestimator

Visionsystem

Cameraχh, χh

χl, χl

hrlc

ah

Figure 2: The architecture of the slung load state estimator.

tor uses a vision based system as the only sensor inputand therefore it does not require any mounting of sen-sors on the load. The vision system uses images froma downwards looking camera to calculate a unit vectorin the helicopter fixed frame pointing from the camerato the load. Furthermore the wire length is estimatedonline and therefore the estimator does not require ex-act knowledge of the suspension system. This makes itideal for augmenting an already autonomous UAV withslung load capabilities.

2.1. Unscented Kalman FilterAn unscented Kalman filter (UKF) is used as the ar-

chitecture for the state estimation. The UKF is a relativenew approach to Kalman filtering which was first pro-posed in Julier and Uhlmann [13] and in recent yearshas been intensively researched for a wide range of esti-mation purposes. It has become quite popular, becauseit in theory yields higher precision than the extendedKalman filter (EKF), as it does not require first-orderlinear approximations. However, this advantage is inmany cases more theoretical that practical as modellinguncertainties are often more significant than linearisa-tion errors (Bisgaard et al. [6]). Nevertheless, the possi-bility of using the nonlinear process and sensor modelsdirectly in the filter is a large advantage in many cases.It should be noted that when using a computational ex-pensive nonlinear model with many states, the UKF be-comes computational expensive.

The UKF is based on the so-called unscented trans-formation, which is used to calculate mean and covari-ance values for a random variable through a determinis-tic sampling approach. This is done by propagating thesystem state vector, using a number of carefully selectedsample points, through the nonlinear model to evaluatethe mean and covariance of the state estimate. The num-ber of selected sample points are equal to 2n+ 1 wheren is the number of states and they are chosen to lie on ahypersphere around the state.

2.2. Process ModelThe system is modeled as a 3-dimensional point mass

pendulum as shown in figure 3 using a wire frame that is

fixed at the wire attachment point and having the z-axispointing along wire. This means that the position of theslung load in the wire frame is defined as

wl =[

0 0 l]T, (1)

wherel is the length of the wire. The position of the loadin the wire fixed frame can is described by the general-ized coordinates (eθw, eφw), which can be considered asa 2-1 Euler angle rotation around the attachment point.This means that the rotation from wire frame to earthframe can be written as

Twe = TTew

=

1 0 00 cos(φw) − sin(φw)0 sin(φw) cos(φw)

cos(θw) 0 − sin(θw)0 1 0

sin(θw) 0 cos(θw)

=

cos(θw) 0 − sin(θw)− sin(φw) sin(θw) cos(φw) − sin(φw) cos(θw)cos(φw) sin(θw) sin(φw) cos(φw) cos(θw)

,

(2)

where it should be noted that the y-axis rotation (eθw)has a different sign definition compared to a standardEuler rotation.

The load position is described using earth fixed co-ordinates as this means that they are independent of thehelicopter attitude changes. The double pendulum mo-

θw

φw

erh

erl

ez

ey

ex

el

hrha

LoadFigure 3: The point mass slung load model.

tion, created by the attitude of the load with respect tothe wire, is neglected, i.e. the load is considered alwaysto be aligned with the wire. Furthermore, the transla-tional accelerations of the helicopter attachment pointgenerated by angular motions are neglected.

As mentioned earlier the slung load estimator is in-tended for augmenting an existing helicopter state esti-mator and is therefore assumed that an adequate filter-ing on the helicopter states have been performed. It is

3

therefore chosen to use the acceleration output of thehelicopter estimator as input to the slung load model.Given the acceleration of the pendulum pivot point, theangular motion can be found as

θ = l−1wx = l−1Tweex (3)

whereθ is a vector of the angular accelerations andxis a vector of the translational acceleration (includinggravity) andl = |el| is the length of the pendulum. Ex-panding yields

eθw =(− cos(θw) cos(φw)exh+

sin(θw) cos(φw)(ezh − g))/l , (4)eφw =(sin(θw) sin(φw)exh − cos(φw)eyh+

cos(θw) sin(φw)(ezh − g))/l , (5)

where [xh yh zh]T are the helicopter translational accel-erations. The position of the load in the earth fixedframe can be found from figure 3 as

erl =el + erh + Teh

hrha , (6)

and load velocities can be found as the differentiation of(6).

2.3. Sensor Model

The output of the vision system is a unit vector (h rlc)pointing towards the load from the camera as shown onfigure 4. The estimated position of the load relative to

Helicopter

Load

hrha

hrhc

hrlc

erh

ezerl e

l

ex

ey

Figure 4: The geometric setup of the sensor model.

the helicopter attachment point (el) can be found from(1) and (2) as

el = Tewwl =

sin(θw) cos(φw)sin(φw)

cos(θw) cos(φw)

l , (7)

The predicted measurement can then be found by off-setting this vector to the camera position (as shown onfigure 4) and normalizing

h rlc =The

el + hrha −hrhc

|Theel + hrha − hrhc|

. (8)

2.4. Vision SystemThe vision system is a camera mounted on the heli-

copter frame looking down on the load. The resultingimage is a top-down view of the load and the groundbelow. To easily identify the load amongst other objectsthat appear in the camera view the load is fitted with avisual marker; in this case a white disk on a black back-ground. The location of the marker in the image is thusan estimate of the position of the load relative to the ori-entation of helicopter.

To identify the marker in the image two circularHough transforms with different radii are usedBallard[2]. A circular Hough transform maps a 2D data setinto another 2D data set such that complete circles aremapped to single points. Since points can be found eas-ily by, for instance, thresholding, it makes the searchfor circles much simpler. The first of the two transformsuses a radius slightly smaller than the white disc markerand triggers on white. The second transform uses a ra-dius slightly bigger than the white disc marker and trig-gers on black. Correlating the two transforms triggersonly those areas where a sufficiently large round whitearea is present and surrounded by a black area. This issufficient to yield a good estimate of the marker loca-tion; as long as the image of the marker is good, i.e. notdistorted by helicopter vibration, this method producesa sub-pixel precision estimate of the marker location.An image from a test flight is shown in figure 5.

Figure 5: Left: Input to the Hough transform; the slung load can beseen in the upper half of the picture. Right: Output of the Houghtransform from which the load can be easily located by a peak detec-tor.

The measurement is checked for a false detection byexamining the pixel detected as the centre of the disk.

4

If it is not sufficiently white it is assumed that the algo-rithm has made a false detection and the measurementis discarded. This could happen if the load is outside thefield of view (FOV) of the camera. Note that the cam-era is fixed to the helicopter which means that both loadswing and helicopter roll and pitch can result in the loaddisappearing from FOV.

It is important to keep the delay in the vision sys-tem low and this is ensured by using the previous es-timate of the location to choose a subset – a region ofinterest (ROI) – of the image for analysis in the nextimage frame. On top of that a threshold is used to sim-ply ignore the pixels that are too far from white to bethe maker. The size of the ROI is a trade-off where asmaller ROI yields a smaller FOV and therefore largerrisk of the load disappearing from FOV, but at the sametime a smaller ROI yields a faster update time on thevision algorithm which gives a smaller risk of the loaddisappearing from FOV.

When the vision algorithm has detected the pixel po-sition of the load this measurement must be mapped toa 3D load position. This is done by first transformingthe pixel position to two angles – a vertical (θp) and ahorizontal (φp) – as shown in figure 6. The camera coor-dinate system is defined to coincide with the helicoptercoordinate system when the camera is pointing forward,i.e. the x-axis is pointing in the image direction. This is

rlc

φp

xc

yc

θp

pz

zc

py LoadCamera viewPerspe tive view

pz

py

ψ amDp Dp

Figure 6: The map of 2D picture position to the 3D spatial location.

done by assuming that the angle from the camera to theload (θp) is proportional to the pixel distance from theload to the image center. This is equivalent to a pin-holelens and neglects optical lens distortion. The distancefrom the image center to the load is found as

Dp =

√

p2y + p2

z . (9)

The angle to the load can then be found as

θp =αFOV

PFOVDp , (10)

whereαFOV is the field of view angle of the camera andPFOV is the number of pixels related to theαFOV. Thehorizontal angle can be found simply by the relationshipbetween thex and they pixel position

φp = arctan(pz/py) . (11)

The unit vector from the camera to the load can then befound in the camera coordinate system and rotated intothe helicopter coordinate system as

hrcl = Thc

cos(θp)sin(θp) cos(φp)sin(θp) sin(φp)

, (12)

whereThc is the direct cosine matrix between the cam-era and the helicopter. The observability of the systemis clear as the vision system directly measures the unitvector pointing to the slung load and the length of thevector can be calculated as show in the following.

2.5. Wire Length EstimationThe pendulous mode frequency of the dual mass he-

licopter slung load system can be determined as

ωn =

√

g(mh +ml)lmh

. (13)

However, if feedback control is applied to the heli-copter, the dual mass system behaviour is altered asthe effect of slung load swing on the helicopter is sup-pressed. The system can then be approximated by astandard pendulum description, which means that thewire length can then be calculated as

l =ω2

n

g. (14)

This frequency is present as a slow sine wave in themeasured load angles (θw and φw), and could be esti-mated using standard FFT (note that it is important touse the measurements transformed into the earth fixedframe to remove helicopter motion from the signals).However, since it is known that the frequency is quitelow and as it is desired to estimate the frequency quickly(i.e. using few samples), a dedicated sine estimator isused. This estimator is a steepest ascent search on (adiscretized version of)

f (ω, θ) =

∫ 2π

0s(t) cos(ωt + θ)dt

∫ 2π

0cos2(ωt + θ)dt

, (15)

wheres(t) is the input signal. This function is the nor-malized inner product between the signal and a lin-early independent (but non-orthogonal) cosine frame,

5

and thus peaks whenω matches the main frequencyof the signal. This method is superior to the oversam-pled FFT when searching for one, approximately knownfrequency, partly because it involves significantly fewercomputations and partly because the oversampled FFTdoes not include normalization at ‘non-integer’ frequen-cies.

However, it is important to use the wire length esti-mator with care: Around hover the oscillations may beso small that it is difficult to detect the correct frequencyand when used in a closed loop system the frequencyof the oscillation can be shifted depending on the con-troller. Therefore, the strategy for using the estimatoris to make a gentle step with the helicopter shortly aftertake off which generates free swing of the slung load.When the sine estimator has converged after a short pe-riod of time, the wire length is locked to the found valueand the state estimates are ready for use in close loop.

The step size of the steepest ascent is the best choiceout of five different predetermined sizes. Typically, themethod converges in 100 - 200 steps, which can be dis-tributed over time as more signal becomes available toavoid high peak load on the computer.

3. Feedforward Control

Damping swing of a slung load is similar to vibrationdamping in many other applications and while actualexamples of slung load anti swing control are rare in theliterature, inspiration can be found in other applications.One of the most obvious applications to draw inspira-tion from is overhead gantry cranes, which exhibit thesame pendulum like behaviour, albeit with much sim-pler actuator dynamics. A commonly used solution tothe swing damping problem is input shaping. The con-cept of input shaping was first suggested in Smith [26].The method was dubbed the Posicast technique and wasbased on the idea of exciting two transient oscillations ina underdamped system such that they cancel each otherand thereby achieving an oscillation free response. In-put shaping has been applied to a range of applicationsapart from cranes, including flexible robotic manipula-tors and space crafts with flexible solar arrays and fuelsloshing. A good introduction to input shaping tech-niques is given in Singh and Singhose [25], where a re-view of input shaping literature is given together with atutorial to practical input shaping design.

A simple way of driving a system with vibration isby using impulses: An impulseA1 is first applied to thesystem which will not only start a motion, but also causea vibration. However, instead of allowing the system

to vibrate, another impulse is applied at an appropri-ate time, which then cancels the vibration. The conceptis illustrated in figure 7 with a undamped second ordersystem with the natural frequencyωn = 1 rad/s.

0 1 2 3 4 5 6 7 8 9 10

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time [s]

Am

plitu

de

A1

A2

A1 response

A2 response

Total response

Figure 7: An undamped second order system driven by two impulsesto achieve a zero vibration response.

To evaluate the performance of applying a sequenceof impulses to cancel vibration a non-dimensional resid-ual vibration term is defined as the vibration ampli-tude cause by impulse sequence normalized with thevibration amplitude cause by unit impulse evaluated atthe time of last impulse in the sequence, which yields(Singh and Singhose [25])

V(ωn, ζ) = eζωntN√

C(ωn, ζ)2 + S(ωn, ζ)2 , (16)

where

C(ωn, ζ) =N∑

i=1

Aieζωnti cos(ωdti) , (17)

S(ωn, ζ) =N∑

i=1

Aieζωnti sin(ωdti) , (18)

whereωn is the natural frequency,ζ is the damping, andωd = ωn

√

1− ζ2 is the damped frequency. To achievea system response with zero residual vibration the im-pulse seriesA1...N that satisfiesV = 0 in (16) must befound. The shortest possible shaper consists of two im-pulses which yields four unknowns:A1, A2, t1, andt2.Solving for these yields

t1 = 0 , t2 =Td

2, A1 =

11+ K

, A2 =K

1+ K. (19)

whereTd is the period of the damped oscillation and

K = exp

−ζπ√

1− ζ2

. (20)

6

3.1. Robust Zero Vibration Command GenerationIn theory, the Zero Vibration (ZV) shaper is capable

of successfully avoiding any oscillation when the nat-ural frequency and damping of the system oscillatorymodes are known. However, in reality, you never haveexact system knowledge which means that there will of-ten be a discrepancy between the actual system and thesystem used for the shaper design. Such a case is illus-trated in figure 8 where the system from figure 7 howhas a 5% error in the frequency. It is clear that while

0 1 2 3 4 5 6 7 8 9 10

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time [s]

Am

plitu

de

A1 A

2

A1 response

A2 response

Total response

0 2 4 6 8 10 12 14

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time [s]

Am

plitu

de

A1

A2

A3

A1 response

A2 response

A3 response

Total response

Figure 8: Response to ZV and robust ZV (ZVD) shaper with 5% fre-quency error.

the residual vibration is somewhat reduced there is stilla significant amount of vibration left and the solutionis to add robustness to the shaper (Singer [24]). Thisresulted in the ZVD shaper which is substantially morerobust to modeling errors as shown to the right in figure8. The shaper is derived by adding the requirement thatthe derivative (thus the D in ZVD) of the residual vibra-tion with respect to the natural frequency and dampingmust be equal to zero

0 =d

dωnV(ωn, ζ) , 0 =

ddζV(ωn, ζ) . (21)

This is achieved by adding an additional impulse to thetwo impulse ZV input shaper, which yields the three

impulse ZVD input shaper. The solution to the ZVDshaper is Singer [24]

t2 =Td

2, t3 = Td , A1 =

11+ 2K + K2

,

A2 =2K

1+ 2K + K2, A3 =

K2

1+ 2K + K2. (22)

The zero derivative constraint makes the slope of theZVD shaper zero at the natural frequency and therebyimproving the robustness of the shaper to modeling er-rors. In figure 9 it is illustrated how robust the ZVDshaper are to errors in damping and frequency.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50

5

10

15

20

25

30

35

40

45

50

Normalized Frequency (ω/ωm

)

Res

idua

l Vib

ratio

n [%

]

ZVD shaper

ζ=0

ζ=0.1

ζ=0.2

Figure 9: Robustness of the ZVD shaper as a function of error indamping (ζ) and frequency (ωn).

3.2. Real-Time Input Shaping

Input shaping is implemented by convolving a se-quence of impulses with any desired command as

∗

C (t) = I ∗ C(t) , (23)

whereC is the initial command,I is the input shaper,

and∗

C is the shaped command. By using a well designedinput shaper, the system will respond to the shaped ref-erence signal without vibration. An input shaper cantherefore be used to filter the reference commands tothe system such that, ideally, swing free motion of theslung load can be achieved.

However, there is a price to be paid for the reduced vi-bration that can be achieved by using the input shapersand especially the robust input shapers. When a com-mand is convolved with an input shaper, the duration ofthe command is extended with the length of the shaper,as illustrated in figure 10. Therefore, it can generallyby said that a longer shaper yields a slower system re-sponse. However, this prolonged response time is mostsignificant for very short manoeuvre commands like a

7

0 2 4 6 8 10 12 140

0.2

0.4

0.6

0.8

1

Ste

p in

put

0 2 4 6 8 10 12 140

0.5

1

1.5

2

Time [s]

Sys

tem

Res

pons

e

Unshaped ZV ZVD

Figure 10: Step inputs and system response without shaping,with ZVand with ZVD shaping.

step. For longer manoeuvres like a flight trajectoryfor the helicopter slung load system, the additional re-sponse time added by the input shaper is insignificant.

3.3. Input Shaping for the Helicopter Slung Load

The use of the input shaper technique to reduce exci-tation of the slung load pendulous modes has the distinctadvantage that there is no need to make preflight tuningof the controller. In section 2.5 it was demonstrated howit is possible to get estimates of the natural frequencyof the pendulum mode. This estimate can be used di-rectly in the input shaper, but is important to rememberthat the estimate represent the damped frequency of thesystemωd and provides no information on the damp-ing ζ. The damping of the slung load motion will varydepending on the aerodynamic drag of the load and onthe interaction with the helicopter. Given these uncer-tainties, a robust shaper seems like the better choice andfrom figure 9 it can be seen that the ZVD shaper seemsquite robust to uncertainties especially in the dampingand this shaper is therefore used for the system.

The input shaper is applied to the entire reference tra-jectory which is necessary for coordinated manoeuvresto keep the synchronization between the different ele-ments. If the input shaper is only applied to parts of thereference vector, these will be delayed compared to theremaining elements.

4. Feedback Control

After having designed the feedforward controller thathelps avoid exciting swing, a feedback controller for ac-tive damping of swing must now be found. A possibilityfor this is the so called delayed controller; the idea with

the delayed controller is that by using intentionally de-layed feedback it is possible to absorb vibrations in aoscillating system. Traditionally, delay in feedback sys-tems is considered problematic and causes deterioratingperformance and even instability, but in this approachthe delay can be used as an advantage. It was first sug-gested in Olgac and Holm-Hansen [19] which considervibration damping in structures where it was denoted‘Delayed Resonator’. The delayed resonator is designedas an oscillator with a natural frequency equal to that ofthe system, and with an appropriate delay this can befed to the system and cancel the system vibrations. Acomparison of the delayed resonator with a standard PDcontroller is made in Elmali et al. [9] and it is concludedthat a comparable performance can be achieved with thetwo. However, the delayed feedback has a number ofadvantages over the PD controller, most prominently theability to incorporate system delays into the controllerwithout loss of performance. This is especially true inthis case where slung load measurements are providedby a vision/image processing system which on systemswith low computational power can result in long de-lays. In Masoud and Nayfeh [15] and Masoud et al. [14]the delayed resonator is used to dampen swing in shipcranes. Also Udwadia and Phohomsiri [27] extends theconcept to consider both negative and positive feedbackand applies it to vibration damping in structures.

4.1. Delayed Feedback Theory

A standard linear second order system is given by

x(t) + 2ωnζ x(t) + ω2nx(t) = u(t) , (24)

whereωn is the natural frequency andζ is the damping.A proportional feedback of the time delayed state valueis introduced as

x(t) + 2ωnζ x(t) + ω2nx(t) = Gdx(t − τd) , (25)

where design parameters of the controller are the gainGd and the time-invariant delayτd. In the Laplace do-main (25) becomes

x(s2 + 2ωnζs+ ω2n) = Gde−τds . (26)

The controller parameters (Gd, τd) must now be foundsuch that the damping of the system is maximised. Moreor less complicated approaches have been suggestedin the literature for this see e.g. Masoud and Nayfeh[15]. However, a simple approach will be proposedhere; model the delay using a Pade approximant (BakerJr and Graves-Morris [1]). The Pade approximant is ac-curate in the magnitude but results in an error in the

8

phase. For a first order approximation the phase erroris close to 5 degrees at the delay frequency while a sec-ond order approximation results in an error of around 2degrees at twice the delay frequency. This is deemed anadequate accuracy for this control system and a secondorder Pade approximation is therefore used

e−τds ≃1− τd/2s+ τ2d/12s2

1+ τd/2s+ τ2d/12s2, (27)

and by using this approximation linear system theorycan be applied to find the appropriate control parame-ters. The delayed feedback controller (C) can be formu-lated in state space form as

C ={

xc = Acxc + Bcuc

yc = Ccxc + Dcuc, (28)

AC =

[

−6/τd −12/τ2d1 0

]

, BC =

[

Gd

0

]

,

CC =[

−12Gd/τd 0]

, DC = 1 .

4.2. Automated Design of the Delayed Feedback Con-troller

The purpose of the controller is to dampen the pen-dulous modes of the slung load within the limits of thehelicopter performance. The design of the controllercan then be formulated as finding the controller param-eter set (Gd, τd) that achieves the maximum damping ofthe pendulous modes while maintaining satisfactory he-licopter behaviour. The controllability of the system isevident from the fact that there is independent controlof the helicopter along in x, y, and z.

Let the linear system

H ={

xh = Ahxh + Bhuh

yh = Chxh + Dhuh, (29)

wherex ∈ Rn is the state vector,u ∈ R

m is the inputvector, andy ∈ R

p is the output vector, be the combinedhelicopter slung load system. By applying the controllerof (28) to the system in positive feedback, the combineddynamics can be found as

At =

[

Ah BhCc

BcCh Ac

]

, xt =

[

xh

xc

]

. (30)

For this system the eigenvalues are given by

(At − λI)xt = 0 , (31)

whereλ ∈ Cn is the vector of eigenvalues with a cor-

responding vectorζ ∈ Rn of dampings. The damping

ζi ∈ ζ of the i’th eigenvalueλi ∈ λ can be found as

ζi =Re(λi)ωni

with ωni = |λi | . (32)

The controller design is then defined as finding the setof control parameters that yields the maximum of thesmallest eigenvalue damping

arg max(Gd,τd)

miniζi . (33)

Given this formulation the process of designing the con-troller can be completely automated using optimization.As the system was assumed to be linear time-invariant itis necessary to redo the design process should the delayparameter change.

4.3. Delayed Feedback for Helicopter Slung Load Sys-tem

The delayed feedback control is well suited for oscil-lation damping in complex systems like the helicopterslung load system as it can account directly for possibledelays in the signal loop which in this case originatesfrom the vision system. It is important to realize thatthis control scheme can not be used for stabilizing thehelicopter or to track trajectories, but simply to dampenload swing. Therefore, an inner loop controller for thehelicopter is assumed as was illustrated in figure 1.

The feedback variables in the helicopter slung loadsystem are the positions of the slung load relative to thehelicopter,xδ andyδ and the output of the controller isadded to the existing reference to the inner loop heli-copter controller. The delayed feedback controller isdefined in the context of (25) as

xr = xr +Gdxδ(t − τ) = xr +Gdl sin(θw(t − τ)) , (34)

yr = yr +Gdyδ(t − τ) = yr +Gdl sin(φw(t − τ)) . (35)

Given a full reference trajectory the velocity referenceare found as time derivatives of (34) and (35)

˜xr = xr +Gdl cos(θw(t − τd))θw(t − τ) , (36)˜yr = yr +Gdl cos(φw(t − τd))φw(t − τ) . (37)

Assuming purely slung load dynamics this means thatthe controller gainGd can be seen as normalized withrespect to the pendulum length. Furthermore, the con-troller delay is defined as normalized with respect to thependulum oscillation periodTn

τd = Tnτn , (38)

where

Tn = 2π

√

lg. (39)

9

Since both controller parameters are defined as normal-ized to the pendulum length the controller can be de-signed for one suspension length and when the length ischanged, the controller is automatically redesigned ac-cordingly. This should in theory mean that the same os-cillation damping is achieved for any suspension length,but in many cases the helicopter dynamics are so slowcompare to the pendulum modes that they cannot be ne-glected. In these cases it is necessary to do a full re-design of the controller for each wire length.

5. Results

The control scheme will here be illustrated use on asmall scale autonomous helicopter: The Aalborg Uni-versity Corona Rapid Prototyping Platform. The AAUCorona is a 1 kg electric indoor helicopter flying witha 0.15 kg slung load in a single 1.25 m wire. It per-forms fully autonomous flight with landings and takeoffusing a set of gain-scheduled PID controllers. A small320x240 pixel downwards looking camera is mountedon the helicopter for the vision system with a 30o FOV.There is no computer onboard the helicopter and allcontrol and estimation computation is done on groundin real time. Sensor information from the helicopteris transmitted to the ground though a wired USB con-nection that hangs from the nose of the helicopter andcontrol signals to the servos are transmitted through thestandard radio control system. Furthermore, helicopterand slung load state measurements are acquired using aVicon motion tracking system at 100 Hz and with a suf-ficient accuracy for these to be considered as truth mea-surements. The motion tracking system is only used forverification purposes and not in the slung load controlfeedback loop.

5.1. Design for Aalborg University Corona

The design for the Corona will only be shown for thelateral dynamics but the process is similar for the lon-gitudinal dynamics. The AAU Corona is controlled bya PID control setup and its dynamic response is closeenough to the slung load dynamics that the feedbackcontroller needs redesign for each wire length.

The damping map for a wire length of 1.25 m isshown in figure 12 and the delayed controller parame-ters is found by the means of a steepest descent methodto

Gd,lat = 0.3 , τn,lat = 0.13 .

The effect of the designed controller on the system dy-namics are illustrated in figure 13 Both the estimator

Figure 11: The Aalborg University Corona flying indoor with slungload.

Gd

τ n

Unstable region

Stable region

0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

0.05

0.1

0.15

0.2

0.25

Figure 12: Damping of the lateral helicopter slung load system as afunction of delayed feedback controller parameters.

and the input shaper do not require any special designas they are independent of the helicopter dynamics.

5.1.1. Controller Enable ProcedureThe procedure for enabling the controller is

Step 1. The helicopter takes off and lifts the slung loadoff the ground.

Step 2. The vision system detects the slung load and en-ables the wire length estimator.

Step 3. The wire length estimator has converged andthe result is used in the state estimator and inputshaper.

Step 4. The wire length is used to calculate the systemdynamics; the values for the delayed controlleris found through a steepest descent search

Step 5. The delayed controller is enabled and therebythe full control scheme is running

10

Figure 13: Pole location for the helicopter slung load with and withoutdelayed feedback.

5.2. Estimator Verification

To verify the design of the estimator and test the per-formance of it, a flight test has been carried out using anumber of very aggressive steps.

Two tests are presented; one with gentle motions tosee how the filter converges and tracks, and one with anaggressive step where the load swings outside the FOVof the camera to test how well the filter can propagatewithout measurements.

This test starts with a take-off where the load is liftedoff the ground by the helicopter. This means that be-fore the load is dragged under the helicopter, the visionsystem cannot see the load. This can be observed inthe first couple of seconds in figure 14 where the esti-mate is fluctuating. After that the vision system sees the

0 2 4 6 8 10 12 14 16 18 20

−0.1

−0.05

0

0.05

0.1

0.15True vs. estimated slung load position

Long

itudi

nal [

m]

0 2 4 6 8 10 12 14 16 18 20

−0.6

−0.4

−0.2

0

0.2

Late

ral [

m]

Time [s]

True Est.

Figure 14: Estimated and true slung load position during takeoff. Notethat the true states actually are high quality measurements from themotion tracking system.

slung load and the estimated states starts to converge.However, it takes some seconds before the estimates are

tracking satisfactorily – this is due to the fact that theestimator is started with a wrong wire length and firstneeds to adjust for this. The convergence of the wirelength estimator can be seen in figure 15 together withthe time between available measurements from the vi-sion system. When the first measurement is availablefrom the vision system the wire length estimator is au-tomatically started with an update frequency of 1 Hzand when it has converged satisfactorily the wire lengthis locked to the converged value. When looking at both

0 2 4 6 8 10 12 14 16 18 200.5

1

1.5

2

2.5Estimated wire length

Wire

leng

th [m

]

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

Tim

e [s

]

Time [s]

Time between vision system measurements

Figure 15: Estimated wire length and time between vision systemmeasurements during takeoff. When the vision system cannot trackthe slung load, the time between measurements increases.

position and velocity estimates (figure 14 and 16) it canbe seen that estimator converge rapidly and tracking thestates satisfactorily.

0 2 4 6 8 10 12 14 16 18 20−0.4

−0.2

0

0.2

0.4True vs. estimated slung load velocity

Long

itudi

nal [

m/s

]

0 2 4 6 8 10 12 14 16 18 20−2

−1

0

1

2

Late

ral [

m/s

]

Time [s]

True Est.

Figure 16: Estimated and true slung load velocities during takeoff

This test is run with an already converged estima-tor and consists of an aggressive 0.8 m right step withthe helicopter. The purpose of this is to create a largeenough swing and/or a large enough tilt of the helicopterfor the load to disappear out of the picture. The esti-

11

mated and true position and velocity are shown in figure17 and 18, from where it can be seen that the estima-tor is capable of propagating the estimates nicely duringthe period without measurements (cf. figure 19). The

0 2 4 6 8 10 12 14 16 18 20−0.4

−0.2

0

0.2

0.4True vs. estimated slung load position

Long

itudi

nal [

m]

0 2 4 6 8 10 12 14 16 18 20−1.5

−1

−0.5

0

Late

ral [

m]

Time [s]

True Est.

Figure 17: Estimated and true slung load position during aggressivestep. The black dots on top of each plot indicates missing vision sys-tem measurements.

0 2 4 6 8 10 12 14 16 18 20−2

−1

0

1

2True vs. estimated slung load velocity

Long

itudi

nal [

m/s

]

0 2 4 6 8 10 12 14 16 18 20−4

−2

0

2

4

Late

ral [

m/s

]

Time [s]

True Est.

Figure 18: Estimated and true slung load velocities during aggressivestep.

measured helicopter accelerations used as input to theprocess model in this test is shown in figure 20.

5.3. Controller Verification

To illustrate the damping effect of the delayed feed-back controller on the AAU Corona two different 1 mlateral manoeuvres are used: A gentle and an aggressiveone. The aggressive manoeuvre is simply a step in po-sition reference, while the gentle one is an accelerationand velocity limited s-curve. The steps are performedboth with and without the delayed feedback controllerand a comparison is shown in figure 21 and 22. As ex-pected the delayed controller is capable of introducing a

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

Tim

e [s

]

Time [s]

Time between vision system measurements

Figure 19: Time between vision system measurements during aggres-sive step.

0 2 4 6 8 10 12 14 16 18 20−4

−2

0

2

4Helicopter accelerations (filter input)

Long

itudi

nal [

m/s

2 ]

0 2 4 6 8 10 12 14 16 18 20−4

−2

0

2

4

Late

ral [

m/s

2 ]

0 2 4 6 8 10 12 14 16 18 20−4

−2

0

2

4

Ver

tical

[m/s

2 ]

Time [s]

Figure 20: Helicopter acceleration used as filter input during aggres-sive step.

significant damping improvement with respect to slungload swing.

Finally, to illustrate the combined effectiveness of thedelayed feedback and the input shaper, an aggressivestep with both controllers enabled is shown in figure 24and 25. Here, a ZVD input shaper is used to shape thestep into a zero residual vibration manoeuvre as is evi-dent on the shaped reference. It can be seen the combi-nation of actively damping swing and avoiding excitingswing during movement results in an almost swing-freemotion.

6. Discussion

It is clear that the control scheme is capable of pro-viding considerable damping of the slung load swingcompared to flight without a dedicated slung load con-troller. There is no doubt that the controller is capable ofavoiding slung load swing almost completely. However,the cost is an additional maneuver time – for short ma-neuver as shown in the results, the rest to rest time forthe helicopter is almost twice as long with the shapercompared to without. When looking at the results itwould be natural to draw the conclusion that the bet-ter damping comes simply from the slower helicopter

12

0 2 4 6 8 10 12 14 16

0

0.5

1

1.5Lateral slungload position (Gentle step)

Pos

ition

[m]

0 2 4 6 8 10 12 14 16

0

0.5

1

1.5Lateral helicopter position (Gentle step)

Pos

ition

[m]

Time [s]

Helicopter reference

Without delayed feedback

With delayed feedback

Figure 21: 1 m gentle lateral step with and without delayed feedback.

0 2 4 6 8 10 12 14 16

0

0.5

1

1.5

Lateral slungload position (Aggressive step)

Pos

ition

[m]

0 2 4 6 8 10 12 14 16

0

0.5

1

1.5

Lateral helicopter position (Aggressive step)

Pos

ition

[m]

Time [s]

Helicopter reference

Without delayed feedback

With delayed feedback

Figure 22: 1 m aggressive lateral step with and without delayed feed-back.

response. However, while slower helicopter motion po-tentially can result in oscillations with smaller ampli-tude, the input shaper ensures that almost all residualoscillations are removed. Furthermore, the input shaperworks for all inputs, slow and fast, and the added ma-neuver time is the same for all inputs. Both the feedfor-ward and the feedback ultimately alters the trajectory ofthe helicopter to avoid and dampen load swing and de-pending on the application these changes could in somecases be unacceptable. A possibility for improvementon the design method could therefore be to integrate adesign factor that directly allows a weighting betweentrajectory changes and slung load swing level.

The input shaping can be robustified against errors insystem damping and oscillation frequency through sac-rifice of system response time. For the delayed feedbackcontroller the robustness qualities are more modest andwhile a robustifying modification to the design methodis proposed in this paper, further attention to this issueis recommended.

0 2 4 6 8 10 12 14 16

−0.4

−0.2

0

0.2

0.4

0.6

Theoretical vs. measured slung load angle (Aggressive step)

Ang

le [r

ad]

Time [s]

TheoreticalMeasured

Figure 23: Comparison of theoretical and measured slung load angleduring aggressive lateral step with delayed feedback.

0 2 4 6 8 10 12 14 16−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Slungload position (Aggressive step)

Late

ral s

lung

load

pos

ition

[m]

Time [s]

Helicopter unshaped reference

Without slungload control

Shaped reference

With feedforward and feedback

Figure 24: Slung load motion for 1 m aggressive step with and withoutdelayed feedback and input shaping.

7. Conclusion

In this paper a swing damping control scheme wasdeveloped to improve slung load flight in autonomoushelicopters. It is designed as an integrated observerand controller scheme and to augment helicopter standalone controllers. A feedforward control scheme basedon input shaping was design to shape trajectories to thesystem in such a way that ideally excitation of slungload swing through manoeuvring is avoided. A feed-back control scheme based on delayed feedback was de-signed to actively dampen out slung swing and when us-ing both simultaneously, virtually swing free slung loadflight can be achieved.

The performance of the control scheme was evalu-ated through flight testing and it was found that the con-trol scheme is capable of yielding a significant reductionin slung load swing over flight without the controllerscheme.

13

0 2 4 6 8 10 12 14 16−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Helicopter position (Aggressive step)

Late

ral h

elic

opte

r po

sitio

n [m

]

Time [s]

Helicopter reference

Without slungload control

Shaped reference

With feedforward and feedback

Figure 25: Helicopter motion 1 m aggressive step with and withoutdelayed feedback and input shaping.

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