Proceedings of the RAAD 201322nd International Workshop on Robotics in Alpe-Adria-Danube Region

September 11-13, 2013, Portoroz, Slovenia

Inertial aided sensor platform stabilization for multirotor aerial vehiclesIgor Cvisica and Ivan Petrovica

aDepartment of Control and Computer Engineering,Faculty of Electrical Engineering and Computing,

University of Zagreb, Unska 3, 10000 Zagreb, CroatiaE-mail: {igor.cvisic,ivan.petrovic}@fer.hr

Abstract. Multiple rotor Unmanned Aerial Vehicles (UAVs) are becoming ubiquitous becauseof their construction simplicity and ease of maintenance. Such UAVs are able to hover, take offand land vertically. In addition, it is straightforward to design an on-board attitude autopilot.In comparison with classical helicopters, multi-rotor aircrafts provide less dangerous testbedin urban and cluttered environments due to their small-size and light-weight blades. In thispaper, we present our prototype of aerial vehicle with eight rotors, which carries a uniqueplatform for exteroceptive sensors. We designed inertial aided stabilization of the movementof the platform, decoupling the motion of exteroceptive sensors from the vehicle motion.This directly contributes to improved position and attitude estimation in visual navigation andsmoother perception of the environment, and indirectly to achievement of the vehicle autonomyin urban and cluttered environments. The functionalities of the prototype aerial vehicle and thestabilizing platform are tested in simulation and experimentally.

Keywords. UAV, multirotor, sensor stabilization

1. Introduction

Multirotor aerial vehicles, with various constructiondesigns, controllers and propulsion systems are takingtheir place amongst hobbyists, government services,industry applications etc. Furthermore, their popu-larity in the research community increased over thelast couple of years. Many authors found theseflying platforms interesting as test platforms for theiralgorithms, but unintentionally ignored the fact thatthese platforms could be very useful in many reallife applications. Many teams have concentrated oncomplex algorithms which can perform fast and high-precision, but mostly not applicable acrobatics. We aremotivated by the idea of enabling those machines to douseful real life tasks, making them safe, autonomous,reliable and competitive for various actions in openspaces and urban areas.

Motivated by this idea we have successfully de-signed and built an autonomous, small areal vehiclewith redundant number of rotors, capable of liftingover 3 kg of payload. This aerial vehicle was used inmany experiments, testing robustness to wind distur-bance, tolerance to motor failure, autonomous flightusing GPS etc. Outdoor environment is very unpre-dictable, and the wind is almost always present, espe-cially at greater altitudes. Therefore, constant varia-tion of vehicle’s attitude, as a reaction to wind gusts,

is inevitable. This can drastically deteriorate the signalquality from exteroceptive sensors. Images from thecamera become blurred, GPS sensor reads Dopplervelocities coupled from vehicle rotation, LIDAR scansare not lines any more etc. This behavior increases theuncertainty of estimated position of the aerial vehicleand distorts the map of surrounding. Some researchesrecover the original signal by compensating it withknown vehicle rotation. If the sensor is a camera,image processing can be used (Wang et al., 2011).But when the obtained image is blurred, the neededinformation is unrecoverable.

Some researches presented their work related tocamera teleoperation, visual servoing and target track-ing. In these papers, image stabilization arose asa secondary problem. Mathematical models are of-ten presented without considering the possibility ofpractical implementation. Equations of motion fora two-axis, pantilt, gimbal system to simplify thegimbal control were presented (Yoon and Lundberg,2001). Problem of camera targeting was presentedin (Chitrakaran et al., 2006) and (Neff et al., 2007)where a camera platform, a quadrotor UAV, and acamera positioning unit are considered to be controlledsimultaneously. The work (Stolle and Rysdyk, 2003)proposed a solution to a problem of limited rangeof a camera mechanical positioner. Software-basedcamera control was presented by (Pieniazek, 2003),

and stabilization for two degree-of-freedom onboardcamera to stabilize the image when the aircraft attitudewas disturbed by turbulence or attitude changes.

In this paper we propose inertial aided stabilizationof the platform with exteroceptive sensors, decouplingits motion from the motion of the vehicle. Sensorstabilization can advance visual navigation in outdoorenvironments, improve position and attitude estima-tion and clarify the perception of environment. Highquality stabilization is obtained with low-cost andeasily available parts, where further improvements arealso possible.

Inertial aided stabilization corrects all types ofdistortions. Also, several sensors can be mountedon the same mechanically decoupled platform. Itprovides unique solution for solving different kinds ofproblems.

2. Standard approach to sensor platformstabilization

Doing experiments with an aerial vehicle in outdoorenvironments, we soon found out that without sensorplatform stabilization it would be difficult to achieveautonomy of the vehicle navigation in outdoor envi-ronments. Our first approach, we named it here asstandard approach, was pretty much straight-forward.We developed a sensor platform with two servo mo-tors, which enabled platform tilting in all directions.By using the information about the roll and pitchangles from existing sensors on aerial vehicle, andby tilting the servo motors for the same amount inthe opposite directions, the platform level could bestabilized. Fig. 1 shows the standard stabilized plat-form prototype. This approach will work well whendynamics of aerial vehicle is low and the movementsare smooth. However, that is usually not the casein outdoor environments and this approach revealstwo major weaknesses - inadequate speed of reactionand backlash. In order to have precise positioningand large torque, servo motors use gears with veryhigh gear ratio. Output shaft has limited rotationalspeed and cannot follow the dynamics of the vehicle.Constant lag is present between the stabilized platformand the aerial vehicle. Second, the attitude of aerial ve-hicle continuously oscillates around the level position,forcing the servo gears to go back and forth and exposeto the backlash. In applications where smooth signalis more important than absolute accuracy, backlashcan be a bigger problem than speed of reaction itself.Beside nonlinearities and sudden jerks, consequencesof the backlash existence are also vibrations in deadband area. Stabilizing platform can move freely inthat band and can easily fall into resonance, especiallyin case of aerial vehicle motors vibration, attitudeoscillation or/and direct wind. Although the deadband is usually measured in tenths of degree, it is

large enough to cause blurred image or to affect lasermeasurement. Fig. 2 shows simulation results of thestabilizing platform angle θ for vehicle oscillations ofangle α with amplitude 45 degrees and frequency 1Hz. It can be seen that amplitude of the platform angleoscillations is about 6 degrees, which is too high.It isimportant to notice that amplitude of the oscillationsfor this stabilization approach would increase withfrequency of vehicle oscillations due to inadequatereaction speed of the servo drives.

Fig. 1. Standard stabilization platform

0 1 2 3 4 5−50

−40

−30

−20

−10

0

10

20

30

40

50

time (s)

angl

e (d

eg)

αΘ

Fig. 2. Standard approach simulation

3. Inertial aided sensor stabilization plat-form

Analyzing the abovedescribed standard stabilizingplatform with two servo motors, one can see thatincreasing the servo speed cannot completely solve theproblem. The problem lays in a fact that, in orderto compensate for the aerial vehicle movement, theinformation is needed that the vehicle movement hashappened. At the moment when this information isreceived by the platform servo control system it is

already too late, as the platform has already moved atleast a little bit together with the vehicle.

In order to avoid direct influence of aerial vehiclerotation to the stabilized platform rotation, one canput the stabilized platform on a gimbal in such a waythat the platform rotates freely in a ball bearings (Fig.3). In ideal case, if one adjusts platforms center ofgravity (CG) with the gimbal axis, linear and rotationalmovement of the vehicle will not disturb the attitudeof the platform. In addition, one can increase themoment of inertia of the platform to create higherresistance to external forces, such as the wind andtension from sensor cables, and produce a smoothermotion. Rotational inertia of the platform can beincreased by separating the platform into two partsof similar weights, mounted on the opposite endsof a pole. Aerial vehicle’s battery can be used asa counterweight to the sensors, and the CG can beadjusted with the position of the battery. In this wayrotational inertia is increased significantly, while thetotal weight is increased only by the mass of the pole.Carbon fiber tube, which is very lightweight, can beused as a pole. Now the rotational dynamics of theplatform is low and external forces can not causesudden change in its attitude. However, those externalforces will act on the platform continuously during theflight, and gradually, platform will drift from desiredposition. Furthermore, in reality, one can not perfectlyalign CG with axis of rotation, and acceleration forceswill also cause undesirable rotational movement of theplatform.

Due to the circumstances described above, somekind of control mechanism for the platform must beimplemented. If we install any hard linkage betweenaerial vehicle and the sensor platform in order tocontrol the platform, vehicle rotation will be directlytransferred to the platform. Therefore, in order to ben-efit from high moment of inertia of the platform, wepropose a soft linkage between the aerial vehicle andthe sensor platform. One way to do this is usage of theelectro-magnetic field, e.g. with a DC motor alignedwith the axis of rotation. If the motor is disconnectedit behaves just like a ball bearing, and the platform canrotate freely. By controlling the motor current, onecan control the torque and compensate for externalforces when necessary. However, in that case motorcan not use gear reduction to produce needed torque,because gears make hard linkage to the aerial vehicle.Motors that create large enough torque directly ontheir output shaft are often too large and heavy foraerial vehicle. Also, motors suffer from cogging, aninteraction between permanent magnets on the rotorand slots on the stator. When disconnected, the motordoes not move freely like the ball bearing. Instead,cogging torque causes jerkiness, which is especiallyprominent at low speeds, such as in this application.

Drawbacks of using gearless motor as soft link-age between the vehicle and the platform, motivate

Fig. 3. Ball bearings with springs on prototype vehicle

our solution, which is moreover much simpler. Weuse springs as the linkage between stabilizing sensorplatform and the vehicle (Fig. 3). One can controlthe attitude of the platform by controlling the tensionof the springs. Unlike motors with cogging, springshave very smooth force curve and cheap servo motorscan be used to control their tension. However, springsdo not completely decouple platform rotation from thevehicle rotation, like disconnected motor in the firstcase. Springs alone just provide a delayed rotationof the platform caused by the vehicle rotation. Onecan use that delay as an elegant solution to a problemof limited reaction speed of the servo drives. Uponsudden change in vehicle’s attitude, at the first momentwhile control system is not able to react, springs willabsorb the energy and high moment of inertia willhold the platform still. Method with springs introducesdelay into the process, which is greater than delayin the control system. This makes control systemvery fast relative to process and solves the problem ofinadequate speed of reaction.

4. Control of the proposed stabilizing plat-form

4.1. Mathematical modelFig. 4 shows the principle of stabilization method inone dimension.

The aerial vehicle and the platform are mechan-ically connected through a common axis of rotationwith the ball bearings. Platform has a servo motorwith the servo arm that can rotate around the sameaxis of rotation as the platform. Angle β betweenthe servo arm and the platform is the angle that wecan control. Tilt of the platform is represented by theangle θ, and we want to keep that angle as close as tozero. During the flight, the vehicle angle α changesthrough the time with a rate proportional to vehicledynamics. We can represent the whole system withthe input angle β, output angle θ and disturbance α.

α

θ

β

r

F1

F2dTaerial vehicle

stabilizingplatform

platform CG

servoarm

Fig. 4. Stabilization platform with springs - principlescheme

Servo arm is connected to the aerial vehicle by twotensional springs with tension forces F1 and F2. Giventhat β =−(θ−α), springs are equal in length, F1 = F2and resulting torque is zero.

Summing the forces on the vehicle in horizontaldirection gives the

(M+m)x+Bx =

−mdθcos(θ)−T sin(α)+dθ2sin(θ),(1)

and summing the moments on the stabilized platformgives

(I +md2)θ+mgdsin(θ)+mdxcos(θ)+bθ =

−2r2ksin(θ+β−α)(2)

where:

- M - mass of the vehicle [kg],

- B - air resistance of the vehicle [ Nsm ],

- m - mass of the stabilized platform [kg],

- m - air resistance of the platform [ Nsm ],

- I - moment of inertia of the platform [kgm2],

- k - spring constant [ Nm ],

- r - half-length of the servo arm [m],

- x - horizontal position of the vehicle [m],

- T - thrust force [N]

- d - distance from platforms CG to the rotationalaxis [m].

The system model (1) and (2) is nonlinear butwe can linearize it. First, the angle of the stabilizedplatform θ will be zero in equilibrium position, duringstabilization it will always follow the zero reference

and we can assume that it will be very close to zero.Therefore, we can write following approximations:

cos(θ)≈1sin(θ)≈θ

θ2≈0.

(3)

Second, since the vehicle equilibrium is hover posi-tion, α = 0, vehicle will mostly operate around hoverposition and in practice α will rarely go beyond 30degrees, the following approximation can be applied:

sin(α)≈α. (4)

Also, for simplicity, we can consider a constant thrust.In practice, multirotor is mostly operating in horizon-tal plane of a fixed altitude, and the thrust is varyingaround the T = (M+m)g. Finally, given the previousdescription of the system itself, we know that theplatform tends to stay still, and the system needs toapply only small corrections against disturbance anddisbalance, with average torque of zero. We canlinearize the right side term of equation (2) aroundthe zero torque β≈− (θ−α) and make an additionalsimplification

sin(θ+β−α)≈θ+β−α. (5)

By applying the above approximations we get themodel linearized around the operating point

(M+m)x+Bx+mdθ+T α = 0, (6)

(I+md2)θ+mgdθ+mdx+bθ+2r2k(θ+β−α) = 0.(7)

Taking the Laplace transform and solving this systemof equations by eliminating x we get the transferfunction of the system

Θ(s) = Gα(s)α(s)−Gβ(s)β(s), (8)

where

Gβ(s) =MmRk

q s+ BRkq

s3 + Mmb+B(I+md2)q s2 + Mm(mdg+Rk)+Bb

q s+ mdgB+BRkq

,

(9)

Gα(s) =(MmRk+T md)

q s+ BRkq

s3 + Mmb+B(I+md2)q s2 + Mm(mdg+Rk)+Bb

q s+ mdgB+BRkq

,

(10)

q = (I +md2)Mm +m2d2, (11)

R = 2r2 (12)

and Mm is the total mass

Mm = M+m. (13)

Also, to have a complete model of the system, we mustmodel the transfer function of the servo used. Ne-glecting the electrical subsystem component of the DCmotor model and representing it only with dominantmechanical subsystem one can write the simplifiedtransfer function of the DC motor

DC(s) =K

τs+1(14)

where K and τ are the dc-gain and the mechanicaltime-constant of the DC motor, respectively. Servois controlling DC motor velocity in its outer positionloop with PD controller. Substituting motor equationabove into PD controller gives transfer function of theservo

A(s) =KKp

τs2 +(1+KKD)s+KKP(15)

where KP and KD are the proportional and derivativecomponent of the PD controller, respectively.

4.2. Feedback control loopBlock diagram of the feedback control of the platformangle θ is depicted in Fig. 5. For controlling theangle θ we have used a controller K(s) of the PIDtype, which parameters are tuned by the autotuningprocedure given in (Peric et al., 1997).

Gα(s)

–

-Θref(s) Θ(s)

+

+

α

Gβ(s)A(s)β

K(s)

δ

-

Fig. 5. Block diagram of the control system

Fig. 6 shows the angle of the stabilized platformin response to disturbance α - aerial vehicle angle.Disturbance is set as a sine with amplitude of 45deg and period of 1 rad/sec. We can see that softestsprings give the best results. However, decreasing thek also decreases the maximal torque we can produce.Relative airflow will produce a drag force on thesensor (Hull, 2007),

Fd =12

ρv2CdA, (16)

where ρ is the density of the fluid, v is the speed ofthe object relative to the fluid, A is the cross-sectionalarea, and Cd is the drag coefficient. Just to be in theright order of magnitude, we have calculated the dragforce for a ball of a radius of 10 cm with a relativeairspeed of 3m/s. We have simulated a short windimpact with resulting drag force applied to the sensor.Results of a simulation test are shown in Fig. 7. Fork = 10 and below system cannot give enough torqueto oppose external forces. Graph also shows that for

k too large system becomes unstable. That is becausePID parameters were constant for all k to emphasizedependence on k. PID tuning should be done afterevery change of k.

0 5 10 15 20−4

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−1

0

1

2

3

time (s)

θ (d

eg)

k=1k=10k=100k=200

Fig. 6. Response to change in vehicles attitude withconstant d

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time (s)

θ (d

eg)

k=10k=50k=100k=200

Fig. 7. Response to external disturbance

4.3. Perfect balanceSetting the perfect balance for the platform woulddecouple rotation of the platform from vehicle accel-eration. Substituting d = 0 into our equations (9),(10)and (11) yields

q = MmI, (17)

Gα(s) =MmRks+BRk

MmIs3 +(Mmb+ IB)s2 +(MmRk+Bb)s+BRk,

(18)Rearranging, we get

Gα(s) =

Rk(Mms+B)Is2(Mms+B)+bs(Mms+B)+Rk(Mms+B)

,(19)

and finally

Gα(s) =Rk

Is2 +bs+Rk. (20)

Equivalently,

Gβ(s) = Gα(s) =Rk

Is2 +bs+Rk. (21)

4.4. Optimal point for center of gravityFig. 8 show dependence of stabilization with respectto various positions for CG. We can see that perfectbalance does not have a minimal error. To obtainthe minimal influence of α on θ one must set thenominator of Gα to zero ( Equation (10)). SinceMmRk >> BRk, neglecting the smaller term gives

MmRk+T md = 0 (22)

In practice, adjusting the CG to

d =−2(M+m)r2kT m

(23)

decreases sensitivity to the change of α. Negatived means that CG should be slightly above the axisof rotation, creating a kind of inverted pendulum.Physically, what happens is that positive angle αcreates a positive torque on the platform through thetension of the springs, but at the same time it projectsthe thrust in horizontal plane that will accelerate thevehicle, and that acceleration force will create negativetorque of the same amount on the platform if d is setaccording to Equation (23). In practice, such precisebalancing is hard to perform and we cannot expect tohave d exactly as we want to. Also, this equation camefrom linearized model and completely canceling theinfluence of α just with selection of d is not possibleneither mathematically.

0 5 10 15 20−4

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−2

−1

0

1

2

3

4

5

time (s)

θ (d

eg)

d=5 mmd=0 mmd=−10 mmd=−20 mm

Fig. 8. Response to change in vehicles attitude withconstant k

Gα(s)

–

-Θref(s) Θ(s)

+

+

α

Gβ(s)A(s)β

K(s)

δ

-+

+

GF(s)

Fig. 9. Block diagram of the control system with thefeedforward loop

4.5. Feedforward control loopSince external disturbance δ cannot be predicted, onlyimprovement we could think of regarding δ would bean aerodynamical case for sensor placement. How-ever, aerial vehicle attitude angle α is known and itsinfluence on θ is predictive. Introducing a feedforwardtransfer function GF one can represent this new systemwith Fig. 9 To cancel out disturbance α followingequation must be satisfied

Gα(s) = GF(s)A(s)Gβ(s) (24)

Solving for GF yields

GF(s) =(MmRk+T md)s+BRk

(MmRk)s+BRk1

A(s)(25)

Looking at equation for A(s), we can see that itmultiplies numerator to have higher order terms thandenominator, making this transfer function impossibleto realize. We will have to simplify A(s) to its constantgain in order to realize GF in practice

A(s)≈1 (26)

to have

GF(s) =(MmRk+T md)s+BRk

(MmRk)s+BRk(27)

Fig. 10 shows simulated response of the system.Note the improvement over the Fig 6. For every selec-tion of k an error is bounded below 0.1 degrees. Fora better comparison, PID parameters are not changedwith introduction of feedforward. In practice, imple-menting a feedforward function requires a knowledgeof d. Easiest way for implementing feedforward issetting the platform close to the perfect balance aspossible, for a feedforward function to become

GF(s) = 1. (28)

5. Experimental results

We have made an experimental platform (see Fig. 11)for presented system. Attitude of stabilized platformis measured with MPU6050 sensor, and the flight con-troller is from our previous work (Cvisic and Petrovic,

0 5 10 15 20−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

time (s)

θ (d

eg)

k=1k=10k=100k=200

Fig. 10. Feed forward response to change in vehiclesattitude

2013). Stabilizing platform controller is tuned withrelay feedback method (Peric et al., 1997). We haveused balanced platform and feedforward with gain of1. Fig. 12 shows platform angle recorded duringthe high frequency disturbance α. We have recordeda platform oscillation with amplitude of approx. 0.3degrees caused by a vehicle oscillation with amplitudearound 20 degrees. Fig. 13 shows 10 seconds longpart of the flight. Platform angle is bounded to halfof degree. Results from experiments are satisfac-tory, although simulation gave slightly better results.We suspect that the main reason for discrepanciesfrom simulation are caused by tension from powercables and disbalance. Vehicle battery is used asa counterweight, and the power cables from batterymust carry out from stabilized platform through thevehicle to the propulsion motors. Although we haveused soft silicone cables arranged to give minimumresistance to movement of the platform, cables mustbe thick enough to carry at least 50 amperes of currentand small tension between vehicle and platform isinevitable. Putting the battery directly on the vehicleand using a dummy weight as a counterweight is notacceptable, because it brings unnecessary weight tothe vehicle, overloads the system, shortens the flighttime and disables the practical use of the vehicle.

6. Conclusion

We have addressed the problem of mounting extero-ceptive sensors on the multirotor aerial vehicles. Wehave analyzed various possible solutions and decidedfor an inertial method with springs. We have set themodel of the system and tested it in a simulator. Thenwe have built a prototype of a stabilization platform,modified the construction of the experimental aerialvehicle to handle the platform and tested the systemin a real outdoor flight. Experimental results showed

Fig. 11. Experimental aerial vehicle in flight

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0

10

20

30

time (s)

angl

e (d

eg)

vehicle pitchplatform pitch

Fig. 12. Platform angle recorded from experiment

slightly greater deviation than expected according tosimulator. We explain that by windy conditions,tension of the power cables and not perfect balance.We would expect much better results if a prototypewould be built with a more precise, industrial gradeparts. Also, enclosing the upper and lower weight inan aerodynamic case would reduce the sensitivity towind. It is convenient to have a modular system thatcan enable the user to mount various types of sensors.That way, the user should re-balance the system byitself and one cannot expect perfect factory balance.For our future work, we consider an online estimatorof the CG from measured angles and accelerations.Then we could use feedforward function to cancel outdisbalance of the platform.

7. Acknowledgments

This work has been supported by the European Com-munitys Seventh Framework Programme under grantagreement no. 285939 (ACROSS).

14 15 16 17 18 19 20 21 22 23

−4

−3

−2

−1

0

1

2

3

4

time (s)

angl

e (d

eg)

vehicle pitchplatform pitch

Fig. 13. Platform angle during the flight

8. References

Chitrakaran, V., Dawson, D. M., and Kannan, H. (2006).Vision assisted autonomous path following for un-manned aerial vehicles. In in Proc of 45th IEEEConference on Decision and Control, pp. 63 - 68,Dec. 2006.

Cvisic, I. and Petrovic, I. (2013). Development and testingof small aerial vehicles with redundant number of

rotors.Hull, D. (2007). Fundamentals of Airplane Flight Mechan-

ics. Springer.Neff, A., Lee, D., Chitrakaran, V., Dawson, D. M., and Burg,

T. C. (2007). Velocity control of a quadrotor uavfly-by-camera interface. In in Proceedings of IEEESoutheast Conference, pp. 273-278, Richmond, VA,Mar. 2007.

Peric, N., Petrovic, I., and Branica, I. (1997). A methodof pid controller autotuning. In Commande dessystemes industrieles - Control of Industrial Systems,Belfort, France, May 20-22, 1997, pp. 43–48.

Pieniazek, J. (2003). Software-based camera stabilizationon unmanned aircraft. In Aircraft Engineering andAerospace Technology: An International Journal,Vol. 75, No. 6, 2003, pp. 575 580.

Stolle, S. and Rysdyk, R. (2003). Flight path followingguidance for unmanned air vehicles with pan-tiltcamera for target observation. In in Proceedings ofthe AIAA Digital Avionics Systems Conference, Oct.2003, pp 01 12.

Wang, Y., Hou, Z., Leman, K., and Chang, R. (2011).Real-time video stabilization for unmanned aerialvehicles.

Yoon, S. and Lundberg, J. B. (2001). Equations of motionfor a two-axes gimbal system. In IEEE Transactionson Aerospace and Electronic Systems, Vol. 37, No.3, July 2001, pp. 1083 1091.