PID UAV

J Intell Robot Syst (2014) 73:261–270DOI 10.1007/s10846-013-9947-y

PID Controller Applied to Hexacopter Flight

Andrea Alaimo · Valeria Artale ·Cristina Lucia Rosa Milazzo ·Angela Ricciardello

Received: 30 August 2013 / Accepted: 13 September 2013 / Published online: 4 October 2013© Springer Science+Business Media Dordrecht 2013

Abstract In the last decades, the increasing inter-est in unmanned aerial vehicles for both militaryand civil applications made necessary the devel-opment of flight control theory and algorithmsmore and more efficient and fast. In this paper, anoriginal trajectory controller, like a ProportionalIntegrative Derivative one, is taken into accountand the drone structure assumes a hexacopterconfiguration, i.e. it consists of six rotors, locatedon the vertices of a regular hexagon with threepairs of counter-rotating fixed pitch blades. Themotion of unmanned aerial vehicle is describedby means of the Newton-Euler equations in termsof quaternions, in order to improve the numeri-cal efficiency and stability of the controller algo-rithm, whose novelty lies in the quaternion error

A. Alaimo · V. Artale · C. L. R. Milazzo ·A. Ricciardello (B)Cittadella Universitaria, 94100 Enna, Italye-mail: [email protected]

A. Alaimoe-mail: [email protected]

V. Artalee-mail: [email protected]

C. L. R. Milazzoe-mail: [email protected]

definition. Both model and algorithm have beentested and then validated through a wide exper-imentation, where the drone keeps going to notelementary trajectories.

Keywords Hexacopter · Newton-Eulerequation · PID controller · Quaternion

Mathematics Subject Classifications (2010)65L05 · 68U20 · 70E15 · 70E60 · 11R52

1 Introduction

The interest of the research community for Un-manned Aerial Vehicle (UAV) design is fastgrowing up with the aim of developing cheaperand more capable machines. Their military andcivil applications vary from surveillance and re-connaissance to search and rescue, but, overall,the main UAV goal is to avoid any risk to aircrew[13, 15, 18].

Thanks to their mechanical structure and con-trol systems, multirotor mikrokopter gain someadvantages over vertical takeoff and landingUAVs [7, 9], that can be summarized as follows.The propeller layout is fixed-pitch based and thecontrol is realized by adjusting the angular veloc-ity of the rotors. This simplifies both the designand maintenance procedures for the vehicle suchthat any complex mechanical system is required

262 J Intell Robot Syst (2014) 73:261–270

for rotor actuation. Moreover, the use of morethan one rotor reduces the length of the bladediameter with respect to a helicopter, leading toless structural and dynamical problems. Further-more, a multirotor UAV can be equipped witha boundary frame at the aim of protecting thewhole structure in case of collision and, thus, ofguaranteeing missions in small and obstacle-denseenvironments, with low risk of damaging the vehi-cle or its surroundings.

Recently, the UAV design moves toward mul-tirotor with more than four rotor, exceeding thequadrotor configuration widely popular in the lastyears [2, 3, 8, 11, 14, 17] due to the possibilityof managing engine failures and increasing thetotal payload. For this reason, in this paper, thecommonly used configuration of a hexacopter istreated. In details, the six-rotors are located on thevertices of a regular hexagon and the propulsionsystem consists of three pairs of counter-rotatingfixed-pitch propellers.

In order to build an appropriate mathemati-cal model the drone is assumed as a rigid body,thus its dynamics can be studied by means ofNewton-Euler differential equations, which con-sider both internal and external influences thataffect the UAV. Actually, the Euler angle para-metrization, which describes the aircraft rotation,is here replaced in dynamical formulation byquaternions, since, contrary to Euler angles, theydo not present any kind of singularity, they showmore efficiency and stability from a computationalpoint of view, and, overall, they provide a quickerresponse [16].

A robust mathematical modeling together withefficient control system guarantees an easy flightmanagement of the drone; for this reason controlstrategies are very frequently research task [12, 15,18, 19]. The Proportional Integrative Derivative(PID) Controller, presented in this work, is basedon quaternion symbolism and differs from theothers thanks to the originality of the quaternionerror, a set of parameters that do not depend onthe trajectory and provide a fast response.

In the following, the mathematical model isbriefly recalled as well as the PID controller, thatrepresents a generalization of the Proportional

Derivative (PD) controller illustrated in [6], is de-scribed. Both mathematical model and controllertechnique are formulated in terms of quaternionas shown in [5]. In conclusion, some trajectories,with several check points, have been chosen asdesired ones for testing and validating both dy-namical model and control system.

2 The Mathematical Model

The aim of this section is to provide the math-ematical equations describing the dynamical be-haviour of the hexacopter by means of a gen-eralization of the quadrotor model presented in[7, 17].

The mathematical model representing thedrone dynamics is deduced from the NewtonEuler equations, since the hexacopter is assumedas a rigid body. It is constituted of six propellerslocated at the vertices of a regular hexagon, suchthat the geometrical symmetry of the structureis preserved. The propulsion system is realizedby means of three pairs of counter-rotating fixedpitch blades in order to facilitate design and main-tenance procedures. The six electric motor dy-namics is relatively fast and therefore it will beneglected as well as the flexibility of the blades.More details are shown in [6].

The quaternion parametrization is applied in-stead of Euler angles for describing the droneorientation because these latter might induce thelost of a degree of freedom in the dynamic systemif the gimbal lock configuration is reached. A com-parison between the two approaches emphasizes agreater efficiency and stability of the quaternionsas well as an increasing gain in time during simu-lations [1, 4]. This latter is a relevant topic in flightcontrol, because a promptness of data processingreflects on an easier manoeuvrability and man-agement especially in case of unexpected eventswhich could damage the stability of the drone. Itis worth to underline that the quaternions and theEuler angles are directly correlated, thus φ, θ andψ can be evaluated through quaternion represen-tation, and vice versa, in order to easier visualizethe drone orientation during flight simulations.

J Intell Robot Syst (2014) 73:261–270 263

As shown in [5], let m be the mass of the drone,ξ its position vector with respect to the inertialframe, Fg the gravitational force, TB the totalthrust, Q the orthogonal transformation matrixfrom the body frame to the inertial one. Totalthrust together with gravitational force representsthe total force acting on the hexacopter, thus, thetranslational component of the motion referred tothe inertial frame can be written as

m ξ = Fg + Q TB. (1)

Let ν be the angular velocity, it satisfies thedifferential equation

I ν + ν × (I ν)+ � = τ B (2)

in which I is diagonal inertial matrix, � representsthe gyroscopic effects and τ B = [

τφ τθ τψ]T the

roll, pitch and yaw moment vector, generated byangular velocity and acceleration of the rotor.

As well, let q be the quaternion vector, whichhas to satisfy the normality condition (i.e. ‖q‖2 =1), than the equation, that governs the rotationaldynamic leads to

q = dd t(S ν) (3)

where S denotes the velocity transformationmatrix.

The differential equations (1), (2) and (3) asso-ciated with null initial condition define the math-ematical model of the hexacopter motion withrespect to the inertial frame. A PID controllertechnique will be applied to the aforesaid initialvalue problem for manoeuvring the drone flightover a certain trajectory.

3 Trajectory Control Model

The trajectory control technique treated in thissection improves the PD controller presented in[6]. In particular, the quaternion approach keepsunchanged, since it reduces the instability dueto the numerical implementation; on the other

hand, an Integrative component has been addedin the flight controller with the aim of reducing theeffects of the fluctuations in hexacopter behaviourcaused by random external forces.

In general, a PID controller assumes the follow-ing form

e(t) = xd(t)− x(t) (4)

u(t) = KP e(t)+ KI

∫ t

0e(s)ds + KD

ddt

e(t) (5)

where u(t) is the control input and e(t) representsthe error function between the desired positionxd(t) and the actual state x(t) . The coefficientsKP,KI,KD represent the parameters for the pro-portional, integrative and derivative components ofthe PID controller.

The PID technique is thus applied to the sys-tems 1 and 2, describing the motion of the aircraftand with respect to the position, it writes

dx = Kx,P (xd − x)+ Kx,D (xd − x)

+Kx,I

∫ t

0(xd − x) ds (6)

dy = Ky,P (yd − y)+ Ky,D (yd − y)

+Kx,I

∫ t

0(yd − y) ds (7)

dz = Kz,P (zd − z)+ Kz,D (zd − z)

+Kx,I+∫ t

0(zd − z) ds (8)

Indeed, differing from classical approachesbased on internal linearization, Lyapunov methodor least square estimations [10, 12, 19], the quater-nion error qe is defined as the difference betweenthe desired orientation and the actual one accord-ing to quaternion algebra. It leads to

qe,1 = −qd,0q1 − qd,3q2 + qd,2q3 + qd,1q0

qe,2 = qd,3q1 − qd,0q2 − qd,1q3 + qd,2q0

qe,3 = −qd,2q1 + qd,1q2 − qd,0q3 + qd,3q0

qe,4 = qd,1q1 + qd,2q2 + qd,3q3 + qd,0q0 (9)


where qd is the quaternion corresponding to thedesired yaw position and q is the quaternion rep-resenting the actual position. Let q0, q1, q2 and thetotal thrust T derived as in [6],

q0 =√√√√

1

2+ dz + g

2√

d2x + d2

y + (dz + g)2− q2

3

T = m(dz + g)

2(q20 + q2

3)− 1(10)

q1 = m(dxq3 − dyq0)

(q20 + q2

3)2T

q2 = m(dxq0 + dyq3)

(q20 + q2

3)2T

The moment components, τφ, τθ , τψ can be com-puted as follows

τφ = (Kφ,D p + Kφ,Pqe,1qe,4

)Ixx (11)

τθ = (Kθ,Dq + 2Kθ,Pqe,2qe,4

)Iyy (12)

τψ = (Kψ,Dr + 2Kψ,Pqe,3qe,4

)Izz. (13)

Through total thrust and φ, θ, ψ moments, thecontrol inputs, i.e. the angular velocities, are soderived

ω21 = T

6k− 2τθ

5kl− τψ

10b, (14)

ω22 = T

6k+ τφ

3kl− τθ

5kl+ τψ

5b, (15)

ω23 = T

6k+ τφ

3kl+ τθ

5kl− τψ

5b, (16)

ω24 = T

6k+ 2τθ

5kl+ τψ

10b, (17)

ω25 = T

6k− τφ

3kl+ τθ

5kl− τψ

5b, (18)

ω26 = T

6k− τφ

3kl− τθ

5kl+ τψ

5b. (19)

Table 1 Parameters con-sidered for the numericalsimulations

k 2.980e-6 [kg m]b 1.140e-7 [kg m2]d 0.225 [m]g 9.81 [m/s2]m 0.468 [kg]Ixx 4.856e-3 [kg m2]Iyy 4.856e-3 [kg m2]Izz 8.801e-3 [kg m2]Ir 3.357e-5 [kg m2]

Let us recall that the hexacopter is controlled byadjusting the angular velocities of the rotors whichare spun by electric motors.

4 Numerical Simulations

This paragraph deals with several numerical simu-lations presented and discussed in order to provethe efficiency, stability and well-working of thealgorithm shown in the previous section. The con-trol algorithm has been codified by using MAT-LAB software and its routine for the integrationof Differential Equations has been employed.

In [6], the PD technique has been applied inorder to control basic trajectories and to analyzethe role played by the angular velocities in theflight, with respect to the symmetry of both trendand structure of the drone. Starting from the sameresults obtained by means of the improved PIDcontroller, in this paper, not elementary trajecto-ries have been chosen with the aim of trying thereliability of the new method.

Given a desired position and orientation, themain idea consists of considering a sequence ofcheck-points along the trajectory and requiringthat the drone passes across them with a certainattitude. The set of physical constants adopted inthe dynamical system during the whole experi-mentation, is reported in Table 1, while the para-meters of the PID controller are shown in Table 2.

Table 2 Constants usedfor the PID controller

i Ki,P Ki,I Ki,D

x 0.2 0.02 0.75y 1 0.13 3.1z 10 5 10φ 0.25 – −0.25θ 0.25 – −0.25ψ 0.3 – −0.25


4.1 First Case

In the first case taken into account, it is requiredthat the aircraft describes a circle at altitude 1.Then, the desired position can be written in aparametric form as follows

⎧⎪⎪⎨

⎪⎪⎩

x =ρ cos(α)

y =ρ sin(α)

z =1

{ρ = 1

α ∈ [0, 2π](20)

Along the trajectory, 81 check points have beenfixed and the orientation required to the drone is20 degrees.

In Fig. 1, the controlled quantities, i.e. x, y,z and ψ , and the control inputs in terms oftotal thrust, are illustrated. In details, Fig. 1(UP-LEFT) shows the actual position of thehexacopter with respect to the XY-plane, at thealtitude z = 1, where symbols locate the fixedcheck-points. The trend of x, y and z componentsof the motion versus time is plotted in Fig. 1(UP-RIGHT) as well as the yaw angle ψ is de-picted in Fig. 1 (DOWN-LEFT) and shows thatthe desired orientation is reached in less then 8seconds. Finally, Fig. 1 (DOWN-RIGHT) depictsthe variation of total thrust in time, emphasizingthat the drone maintains the hoovering conditionduring the whole simulation.

−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

1.5

time [s]

posi

tion

[m]

XdX

0 500 1000 1500 2000 2500 3000 3500

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

time [s]

posi

tion

[m]

xyz

0 2 4 6 8 100

5

10

15

20

25

time [s]

Yaw

ang

le [

deg]

yaw

0 500 1000 1500 2000 2500 3000 35004.591

4.5912

4.5914

4.5916

4.5918

4.592

4.5922

time [s]

Thr

ust [

N]

Fig. 1 Case 1: UP the Figure shows desired position () and actual position (continuous line) in the XY plane (left) and thethree component of the drone motion (right); down the Figure illustrates the yaw angle (left) and the total Thrust (right)


4.2 Second Case

In the second case the circular configuration iscomplicated through the presence of several circlecombined such that the desired position leads tothe following parametric function

⎧⎪⎪⎨

⎪⎪⎩

x = cos(aα)− cos3(bα)

y = sin(cα)− sin3(dα)

z =1

α ∈ [0, 2π] . (21)

Two different cases have been analysed by varyingthe coefficients a, b , c, d as a = 3, b = 1, c = 3,d = 1, firstly, and a = 5, b = 1, c = 5, d = 1, later.

Hexacopter position and attitude correspond-ing to both simulations are reported in Figs. 2and 3 respectively.

Along the two trajectories, 121 check pointshave been fixed and the orientation required tothe drone is again 20 degrees.

In Fig. 2, where the desired position correspondsto a = 3, b = 1, c = 3, d = 1, the actual position ofthe aircraft is reported distinguishing the move-ment in the XY-plane, with also the check-points(LEFT), from the x, y and z evolution in time(RIGHT). The other controlled variable is theyaw angle ψ , depicted in Fig. 2 (DOWN-LEFT)showing that the 20 degrees in orientation isreached in less then 8 s. Finally, Fig. 2 (DOWN-

−1.5 −1 −0.5 0 0.5 1 1.5−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

time [s]

posi

tion

[m]

XdX

0 1000 2000 3000 4000 5000−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

time [s]

posi

tion

[m]

xyz

0 2 4 6 8 100

5

10

15

20

25

time [s]

Yaw

ang

le [

deg]

yaw

0 1000 2000 3000 4000 5000

4.591

4.5912

4.5914

4.5916

4.5918

4.592

4.5922

4.5924

time [s]

Thr

ust [

N]

Fig. 2 Case 2.1: UP the Figure shows desired positioncorresponding to a = 3,b = 1, c = 3,d = 1. () and actualposition (continuous line) in the XY plane (left) and the

three component of the drone motion (right); down theFigure illustrates the yaw angle (left) and the total Thrust(right)


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

time [s]

posi

tion

[m]

XdX

0 1000 2000 3000 4000 5000−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

time [s]

posi

tion

[m]

xyz

0 2 4 6 8 100

5

10

15

20

25

time [s]

Yaw

ang

le [

deg]

yaw

0 1000 2000 3000 4000 50004.5905

4.591

4.5915

4.592

4.5925

4.593

4.5935

4.594

time [s]

Thr

ust [

N]

Fig. 3 Case 2.2: UP the Figure shows desired positioncorresponding to a = 5,b = 1, c = 5,d = 1. () and actualposition (continuous line) in the XY plane (left) and the

three component of the drone motion (right); down theFigure illustrates the yaw angle (left) and the total Thrust(right)

RIGHT) depicts the sum of the control inputs,that is the variation of total thrust in time. Again,the drone maintains the hoovering condition dur-ing the whole simulation.

Analogously to the fist simulation of the secondcase, Fig. 3 (UP-LEFT) depicts the desired po-sition corresponding to a = 5, b = 1, c = 5, d = 1,marked by and the actual position of the aircraftin the XY-plane (line); Fig. 3 (UP-RIGHT) illus-trates the motion of the three components versustime. The desired attitude is also reached in fewsecond as shown in Fig. 3 (DOWN-LEFT) as wellas the maintaining of hoovering can be deducedby Fig. 3 (DOWN-RIGHT).

4.3 Third Case

In conclusion of the numerical simulation section,in order to describe a not elementary trajectorydifferent from the circular ones treated until now,a star shape path has been considered. Its para-metric function follows⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

x=(a−b) cos(α)+b cos(α

( ab

−1))

y=(a−b) sin(α)−b cos(α

( ab

−1))

z=1

α∈ [0, nπ]

(22)


in which two different sets of coefficients a, b , nhave been selected and similar to the previoussimulations, controlled variables and control in-puts are discussed.

The first case corresponds to the choice a/b =2.5, b = 1, n = 8, and it is depicted in Fig. 4 (UP-LEFT) by means of its 161 check points; thecontinuous line indicates the solution of the PIDcontrol that is the actual position described by thedrone. The trend of displacement (UP-RIGHT)and bearing (DOWN-LEFT) is represented inFig. 4 for about 5,000 s. The role of the angularvelocities is exhibited by the total thrust in Fig. 4

(DOWN-RIGHT). Figure 5 displays the secondcase corresponding to a/b = 1.8, b = 1, n = 10.Along the desired trajectory, 161 check pointsare determined and put out through markers inFig. 5 (UP-LEFT) where the continuous line is theplane curve describing the actual position of thedrone in XY plane. Figure 5 exhibits the evolutionin time of position and of attitude by means ofx, y and z functions of the motion (UP-RIGHT)and the yaw angle (DOWN-LEFT). Finally, Fig. 5(DOWN-RIGHT) depicts the whole action of theangular velocities which guarantee the hooveringstate during the flight.

−3 −2 −1 0 1 2 3 4−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

time [s]

posi

tion

[m]

XdX

0 1000 2000 3000 4000 5000 6000 7000−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

time [s]

posi

tion

[m]

xyz

0 2 4 6 8 100

5

10

15

20

25

time [s]

Yaw

ang

le [

deg]

yaw

0 1000 2000 3000 4000 5000 6000 70004.59

4.591

4.592

4.593

4.594

4.595

4.596

4.597

time [s]

Thr

ust [

N]

Fig. 4 Case 3.1: UP the Figure shows desired position cor-responding to a = 2.5,b = 1,n = 8 () and actual position(continuous line) in the XY plane (left) and the three

component of the drone motion (right); down the Figureillustrates the yaw angle (left) and the total Thrust (right)


−2 −1 0 1 2 3−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

time [s]

posi

tion

[m]

XdX

0 1000 2000 3000 4000 5000 6000 7000−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

time [s]

posi

tion

[m]

xyz

0 2 4 6 8 100

5

10

15

20

25

time [s]

Yaw

ang

le [

deg]

yaw

0 1000 2000 3000 4000 5000 6000 70004.5905

4.591

4.5915

4.592

4.5925

4.593

4.5935

4.594

4.5945

time [s]

Thr

ust [

N]

Fig. 5 Case 3.2: UP the Figure shows desired position cor-responding to a = 1.8,b = 1,n = 10 () and actual position(continuous line) in the XY plane (left) and the three

component of the drone motion (right); down the Figureillustrates the yaw angle (left) and the total Thrust (right)

5 Concluding Remarks

An efficient and reliable PID technique based onquaternion for a hexacopter control and stabiliza-tion has been presented and discussed by means ofa wide experimentation. The PID controlled hasbeen applied to Newton-Euler equations, describ-ing the dynamical behaviour of the hexacopter.Numerical results emphasized that actual positiongained by the numerical integration of the dynam-ical system, overlaps the check-points fixed alongthe path of the desired position. Moreover, therequired attitude is reached in few seconds and

the hoovering state is preserved during the entireflight. The PID controller parameters do not varywith the desired position. These promising resultsinduce to an implementation of the presentedtechnique in real flights, where rapid and reliableresponses of the controller are necessary to ma-noeuvre and manage the UAVs.

Acknowledgements Project supported by the PO. FESR2007/2013 subprogram 4.1.1.1 “Actions to support the re-search and experimental development in connection withthe production sectors, technological and production dis-tricts in areas of potentiality excellence that test high inte-gration between universities, research centers, SMEs and


large enterprises”; (Prog. “Mezzo Aereo a controllo re-moto per il Rilevamento del TErritorio - MARTE” GrantNo.10772131).

References

1. Alaimo, A., Artale, V., Milazzo, C.L.R., Ricciardello,A.: Comparison between euler and quaternion para-metrization in uav dynamics. In: AIP Conference Pro-ceedings (2013)

2. Artale, V., Barbaraci, G., Milazzo, C.L.R., Orlando, C.,Ricciardello, A.: Dynamic analysis of a hexacopter con-trolled via LQR-PI. In: AIP Conference Proceedings(2013)

3. Artale, V., Collotta, M., Pau, G., Ricciardello, A.:Hexacopter Trajectory Control using a Neural Net-work. In: AIP Conference Proceedings (2013)

4. Artale, V., Milazzo, C., Ricciardello, A.: An example ofquaternion parameterization for dynamical simulation.In: International Conference on Mathematical Model-ing in Physical Sciences, IC-MSQUARE ConferenceProceedings Book (2013)

5. Artale, V., Milazzo, C., Ricciardello, A.: Mathematicalmodeling of hexacopter. Appl. Math. Sci. 7(97), 4805–4811 (2013)

6. Alaimo, A., Artale, V., Milazzo, C., Ricciardello,A., Trefiletti, L.: Mathematical modeling and controlof a hexacopter. In: ICUAS’13 Conference DigitalProceedings Simulator Aero Model Implementation(2013)

7. Alderete, T.S.: Simulator aero model implementation,NASA Ref. Pub. 1373, DOT/FAA/CT-94/83 (1995).Available online: www.aviationsystemsdivision.arc.nasa.gov/publications/hitl/rtsim/Toms.pdf. Accessed 7 Nov2011

8. Castillo, P., Lozano, R., Dzul, A.: Modelling andcontrol of mini-flying machines. Springer, New York(2005)

9. Hoffmann, G.M., Huang, H., Waslander, S.L., Tomlin,C.J.: Quadrotor helicopter flight dynamics and control:theory and experiment. In: Proceedings of the AIAA

Guidance, Navigation and Control Conference andExhibit (2007)

10. Kristiansen, R., Nicklasson, P.J.: Satellite attitude con-trol by Quaternion-Based backstepping. In: Proceed-ings of the 2005 American Control Conference (2005)

11. Mc Kerrow, P.: Modelling the Draganflyer four-rotorhelicopter. In: Proceedings of the 2004 InternationalConference on Robotics & Automation, pp. 3596–3600. N. Orleans, LA:IEEE (2004)

12. Mian, A.A., Daoboo, W.: Modeling and Backstepping-based Nonlinear Control Strategy for a 6 DOFQuadrotor Helicopter. Chin. J. Aeronaut. 21, 261–268(2008)

13. Morse, B.S., Engh, C.H., Goodrich, M.A.: UAV videocoverage quality maps and prioritized indexing forwilderness search and rescue. In: HRI’10 Proceed-ings of the 5th ACM/IEE International Conference onHuman-Robot Interaction (2010)

14. Pounds, P., Mahony, R., Corke, P.: Modelling and con-trol of a large quadrotor robot. Control. Eng. Pract. 18,691–699 (2010)

15. Rango, A., Laliberte, A., Herrick, J.E., Winters,C., Havstad, K., Steele, C., Browning, D.: Un-manned aerial vehicle-based remote sensing for range-land assessment, monitoring and management. J.Appl. Remote. Sens. 3(1), 033542-033542-15 (2009).doi:10.1117/1.3216822

16. Rico-Martinez, J.M., Gallardo-Alvarado, J.: A simplemethod for the determination of angular velocity andacceleration of a spherical motion through quaternions.Meccanica 35, 111–118 (2000)

17. Salazar, S., Romero, H., Lozano, R., Castillo, P.: Mod-eling and real-time stabilization of an aircraft hav-ing eight rotors. J. Intell. Robot. Syst. 54 455–470(2009)

18. Waharte, S., Trigoni, N.: Supporting search and rescueoperations with UAVs. In: EST’10 Proceedings of the2010 International Conference on Emerging SecurityTechnologies (2010)

19. Zhang, R., Quan, Q., Cai, K.Y.: Attitude control ofquadrotor aircraft subject to a class of time-varyingdisturbances. IET Control Theory Appl. 5, 1140–1146(2011)

http://www.aviationsystemsdivision.arc.nasa.gov/publications/hitl/rtsim/Toms.pdf

http://www.aviationsystemsdivision.arc.nasa.gov/publications/hitl/rtsim/Toms.pdf

http://dx.doi.org/10.1117/1.3216822

PID UAV

Documents

Transcript of PID UAV