Research ArticleDynamical Modelling and Robust Control for an UnmannedAerial Robot Using Hexarotor with 2-DOF Manipulator

Li Ding 1 and Hongtao Wu2

1College of Mechanical Engineering, Jiangsu University of Technology, No. 1801 Zhongwu Street, Changzhou, China2College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street,Nanjing, China

Correspondence should be addressed to Li Ding; nuaadli@163.com

Received 6 May 2019; Accepted 9 September 2019; Published 21 October 2019

Academic Editor: Jacopo Serafini

Copyright © 2019 Li Ding and Hongtao Wu. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

The robust control issues in trajectory tracking of an unmanned aerial robot (UAR) are challenging tasks due to strong parametricuncertainties, large nonlinearities, and high couplings in robot dynamics. This paper investigates the dynamical modelling androbust control of an aerial robot using a hexarotor with a 2-degrees-of-freedom (DOF) manipulator in a complex aerialenvironment. Firstly, the kinematic model and dynamic model of the aerial robot are developed by the Euler-Lagrange method.Afterwards, a linear active disturbance rejection control is designed for the robot to achieve a high-accuracy trajectory trackinggoal under heavy lumped disturbances. In this control scheme, the modelling uncertainties and external disturbances areestimated by a linear extended state observer, and the high tracking precision is guaranteed by a proportion-differentiation (PD)feedback control law. Meanwhile, an artificial intelligence algorithm is applied to adjust the control parameters and ensure thatthe state variables of the robot converge to the references smoothly. Furthermore, it requires no detailed knowledge of thebounds on unknown dynamical parameters. Lastly, numerical simulations and experiments validate the efficiency andadvantages of the proposed method.

1. Introduction

Recently the capability of UARs has been expanded radicallywith multidegrees-of-freedom aerial manipulators. The mostattractive aspect of UARs is that they have enormous poten-tial in interacting with the environment, such as taking sam-ples of material from areas difficult to access, inspection andmaintenance of high power lines, and transporting a payload.As a typical nonlinear and coupled system, several worksabout the UARs have been reported in the literature con-cerning kinematics and dynamics [1, 2], trajectory planning[3], control [4, 5], and cooperation [6]. In these works, thehigh-performance manipulation capacity of the UARsdepends on an appropriate flight controller. However, theflight controller designers must have a good understandingof a wide range of disciplines, including flight dynamics,robotics, control theory, simulation analysis, and verificationand validation. Therefore, it is a challenge for researchers to

design a satisfied controller. This paper provides some discus-sion about the issues in dynamical modelling and robust con-troller of a UAR using a hexarotor with 2-DOF manipulator.

First of all, the complexity in modelling of UARs mainlyarises from the coupled dynamics between the aircraft andthe manipulator. For example, the roll inputs can producepitch responses as large as the pitch responses. Aircraftmotion can produce a very large manipulator motion. Hence,the coupling effect may cause a change in the physical param-eters of the system during the operating process. Aiming atthis issue, the aerial robot is divided into two subsystems,namely, the aircraft and the manipulator. The coupling effectof the two subsystems was regarded as an external distur-bance. For example, Orsag et al. [7] had analysed the internalrelationship between the manipulator and the aircraft todevelop the dynamic models of the two subsystems by theNewton-Euler method. Pounds and Dollar [8] used theLagrange method to obtain the dynamic model of an aerial

HindawiInternational Journal of Aerospace EngineeringVolume 2019, Article ID 5483073, 12 pageshttps://doi.org/10.1155/2019/5483073

robot, of which the single-DOF manipulator was treated as avariable load. On the contrary, some researchers treated thecoupling effect as modelling uncertainties so that an inte-grated model could be established. For example, Ding andYu [9] regarded the forces and torques of the manipulatoras the total disturbances and considered the entire aerialrobot system as a single rigid body to obtain its kinematicsand dynamics. Abaunza et al. [10] adopted a dual quaternionmethod to generate the dynamic model of an aerial robotusing a quadrotor with a 3-DOF manipulator. In this paper,the latter scheme is chosen to obtain the dynamic model ofan aerial robot using a hexarotor with a 2-DOF manipulatorbased on the Euler-Lagrange method.

The design of a flight control system is another issue.The applications of UARs strongly depend on the fact thatmovement of the aircraft is satisfactorily stabilized. Indeed,if the position or attitude of the aircraft is not controlledwith high precision, the equipped manipulator will suffervibration and give up the operating task. Meanwhile, theinfluence of unknown environment and the interactionamong different subsystems have to be carried out. More-over, the controller design process should seek a methodto balance the trade-offs between stability, performance met-rics, and robustness to noise and uncertainties. Satisfyingexternal constraints and considering the dynamical natureof the aerial robot system, robust control of the UARs is stillan open problem.

The robust control issue can be handled using the follow-ing two approaches, termed the model-based approach andthe model-free approach. In the former approach, the fullinformation about the aerial robot plant should be known apriori. Accordingly, a subsystem (state observer [11], outputobserver [12], Kalman’s filter [13], etc.) is built, which recon-structs the plant output and rejects the disturbances. Thesecontrol laws are parameterized based on the known model,such as the linear quadratic control (LQR) [14], modelpredictive control (MPC) [15], and H∞ control [16]. It isobvious that constructing these control laws requires contin-uously updated information about the working model of theplant in the real-time implementation. The aftereffects of anyoccurring instability are then accommodated using a highgain. In that case, undesirable transients may occur, whichcauses saturation of actuators and damage to the componentsin the system. On the other hand, the model-free approachbecomes an alternative way to design a control law basedon the data of input and output. It is deemed more conve-nient than the model-based approach, which attracts manyresearchers to focus on it. For example, a proportional inte-gral derivative (PID) control structure for a quadrotor withlightweight manipulator was discussed in Ref. [17]. The pro-posed controller could compensate for the reactionary forcesduring both flight and manipulation. In Ref. [18], Kim et al.proposed an adaptive sliding mode controller (SMC) for acooperative aerial manipulation to manipulate the pose ofthe object, which is also verified by simulations and experi-ments. Jimenez-Cano et al. [2] designed a variable parameterintegral backstepping controller for an unmanned helicopterequipped with robotic multilink arms, and the effectivenessof this controller was verified in simulation.

In the aerial control system application, it is also impor-tant to suppress the response to lumped disturbances. A goodexample of this was in the development of a robust controllaw, where relevant controller design adopted the linearactive disturbance rejection control (LADRC) [19–21]. Thistechnique utilizes a linear extended state observer (LESO)to estimate the lumped disturbances and adopts a propor-tional derivative (PD) control law to ensure convergence ofthe system output. However, the linear methods cannotafford satisfactory trajectory tracking performance for UARswith high nonlinearity under large motion envelope. Themain contributions of this paper are threefold. Firstly, a sys-tem model of a UAR including kinematics and dynamics hasbeen established. Secondly, a LADRC is developed for trajec-tory tracking control of a UAR, where a LESO is used to esti-mate the disturbances. Meanwhile, an artificial intelligencealgorithm called the artificial bee colony (ABC) algorithm isintroduced to adjust the control parameters of LADRC.Thirdly, the proposed method is investigated by a series ofsimulations and experiments. To the best of our knowledge,no reports on robust control using LADRC for the UAR areavailable until now.

The outline of this paper is arranged as follows. The sys-tem modelling of the aerial robot by the Euler-Lagrangemethod is described in Section 2. In Section 3, a robust con-trol strategy is presented. Stability analysis and parametertuning of the control system are illustrated in Section 4.Meanwhile, comparative simulations are performed to dem-onstrate the effectiveness of theproposed controller.Anexper-imental validation with flight tests is provided in Section 5.Finally, some conclusions and contributions are summarizedin Section 6.

2. System Description

2.1. Kinematics. As depicted in Figure 1, there are threecoordinate frames in the UAR system: the earth-fixedframe fIg, body-fixed frame fBg, and manipulator-fixedframe fMgðM = 1, 2, eÞ. Let the generalized coordinate ofthe aerial robot be expressed by

q = pT ,ΩT ,ΘT� �T = x, y, z, ψ, θ, ϕ, ε1, ε2½ �T ∈R8×1, ð1Þ

where p = ½x, y, z�T and Ω = ½ϕ, θ, ψ�T denote the positionand the Euler angles of the hexarotor in the inertial frame,respectively. Furthermore, ϕ is the roll angle, θ is the pitchangle, and ψ is the yaw angle. The vector Θ = ½ε1, ε2�T rep-resents the joint angles of the 2-DOF manipulator.

Using the rotation matrix IRB, the linear velocity B _P ofthe frame fBg is written relative to the frame fIg as

_p = IRBB _p: ð2Þ

Similarly, let ω denote the angular velocity in the framefIg. The angular velocity Bω of the frame fBg is expressedrelative to the frame fIg as

ω = IRBBω: ð3Þ

2 International Journal of Aerospace Engineering

Besides, the Euler angular rate _Ω can be transformedto the angular velocity ω by the standard kinematic rela-tionship:

ω = T _Ω, ð4Þ

where T is the transformation matrix.Substituting equation (4) to equation (3), one obtains

Bω = IRBTT _Ω: ð5Þ

Subsequently, the centre of mass of the link iði = 1, 2Þ iscomputed as

Ipi = IRBBp + Bpi� �

= p + IRBBpi: ð6Þ

To determine the relationship among the joint veloc-ity B _pi, angular velocity Bωi, and end-effector velocity _Θ,one gets

B _pi = JP Θð Þ _Θ,Bωi = JO Θð Þ _Θ,

(ð7Þ

where JPðΘÞ and JOðΘÞ are the manipulator Jacobianmatrix. The calculation of the Jacobian is referred toRef. [22].

Then, the linear velocity and angular velocity relative tothe frame fIg are concluded as

I _pi = _p + S ωð ÞIRBBpi + IRBJP Θð Þ _Θ,

Iωi = ω + IRBJO Θð Þ _Θ,

(ð8Þ

where Sð⋅Þ is the skew-symmetric matrix.For the sake of simplicity, the kinematic model using a

matrix form is described as

_p

ω

I _piIωi

2666664

3777775 =

I3×3 03×3 03×203×3 T 03×2I3×3 −S IRB

Bpi� �

T IRBJP Θð Þ03×3 T IRBJO Θð Þ

2666664

3777775q =

A1

A2

A3

A4

2666664

3777775 _q:

ð9Þ

2.2. Dynamics. To describe the relationship between inputsand motion of the aerial robot, the dynamic model derivedby the Lagrange equation is given by [23]

ddt

∂L∂ _q

� �T

−∂L∂q

� �T

= τ + τD, ð10Þ

L = K −U , ð11Þwhere τ is the generalized torque associated with the general-ized coordinate. τD indicates external disturbance applied tothe system. L is the Lagrangian expressed as the differencebetween kinetic energy K and potential energy U .

The kinematic energy is governed by the sum of themotion of the hexarotor and manipulator, which is written as

K = KB + 〠2

i=1Ki, ð12Þ

where

KB =12mB _pT _p +

12_ΩTTT IRBIB

IRTi T _Ω, ð13Þ

Ki =12mi

I _piT I _pi +

12Iω

TiIRiIi

IRTiIωi, ð14Þ

where m and I are mass and inertia moment, respectively.As done for kinematic energy, the potential energy stored

in the aerial robot is given by

U =mBgeT3 p + 〠2

i=1migeT3 p + IRB

Bpi� �

, ð15Þ

where e3 = ½0, 0, 1�T and g is the gravity.Introduce equations (11)-(15) into equation (10), yielding

M qð Þ€q +C q, _qð Þ _q +G qð Þ = τ + τD, ð16Þ

zI

xI

yI

oI

{I}

zB

xB

yB

oB

{B}

y1z1

x1

{1}

x2z2 y2

{2} {e}

ze y

e

xe

Figure 1: Reference frames and vectors of our UAR.

3International Journal of Aerospace Engineering

where the inertiamatrixMðqÞ, theCoriolismatrixCðq, _qÞ, andthe gravity matrixGðqÞ are calculated as

M qð Þ =AT1mBA1 +AT

2IRBIB

IRTBA2

+ 〠2

i=1AT3miA3 +AT

4IRiIi

IRTi A4

n o,

ð17Þ

C q, _qð Þ _q = _M qð Þ _q − 12

∂∂q

_qTM qð Þ _q� �� �T

, ð18Þ

G qð Þ = ∂U∂q

: ð19Þ

In thedynamicmodel, the generalized torque contains twocomponents.Regarding the joint torque, each joint isdrivenbyan actuator (direct drive or gear drive). Indeed, the torquecould be calculated through the current and torque constant[24]. With respect to the hexarotor, the forces and torquesactuated by six propellers are expressed in the following form:

F = 〠6

i=1f i,

τϕ = f1 + f3 − f4 − f6ð Þ sin π

6 + f2 − f5h i

⋅ l,

τθ = f3 + f4 − f1 − f6ð Þ sin π

3 ⋅ l,τψ = τm1 + τm3 + τm5 − τm2 − τm4 − τm6,

8>>>>>>>>>><>>>>>>>>>>:

ð20Þ

where f iði = 1,⋯,6Þandτmiði = 1,⋯,6Þare thrust andmomentproduced by themotors, respectively. l is the lever length fromthe centre of a propeller to the centre of the vehicle body.

Since the hexarotor flies in a trimmed condition, itsdynamic model can be reduced into a simplified form[25, 26]. Therefore, the nominal relation of the inputs tothe aerial robot and generalized torque is rewritten as:

τ =N3×1 03×3 03×203×1 TT IRB 03×202×1 02×3 I2×2

2664

3775

F

τϕ

τθ

τψ

τε1

τε2

2666666666664

3777777777775, ð21Þ

where

N = θ cos ψ + ϕ sin ψ, θ sin ψ − ϕ cos ψ, 1½ �T : ð22Þ

3. Robust Control Strategy

From the relation of the aerial robot displayed in equations(10)-(21), the input and output present a second-order deriv-ative relation, which is shown in Figure 2. In other words, thedynamic model of the aerial robot can be regarded as eight

second-order subsystems. In this section, the design of aLADRC for each subsystem will be introduced.

Consider a second-order plant:

€xs = f s xs, _xs,ws, tð Þ + bu,ys = xs,

(ð23Þ

where xs, u, and ys are the state variable, system input, andsystem output, respectively.

Suppose b0 is the approximate value of b, system (23) isrewritten as

€xs = f s + b − b0ð Þu + b0u = f + b0u,ys = xs:

(ð24Þ

Remark 1. The lumped disturbance f is another form of theterm f sðxs, _xs,ws, tÞ, which contains parametric uncertainties,external disturbance, and complex nonlinear dynamics.

Assumption 1. Assume that the lumped disturbance f is dif-ferentiable and bounded. It indicates k f k <∞ and k _f k <∞,and their bounds are defined as supt>0k f k = f b and supt>0k _f k = hb, respectively.

Using a state-space form to describe the system (24) yields

_x =Ax + Bu + Eh,y = Cx,

(ð25Þ

where

A =0 1 00 0 10 0 0

2664

3775, ð26Þ

B =0b0

0

2664

3775, ð27Þ

Input OutputF x

y

z

𝜓

𝜙

𝜖1𝜖2

𝜃q=‥

‥

‥

‥

‥

‥

‥

‥

‥

F

F

𝜏𝜓𝜏 =Δ

𝜏𝜙

𝜏𝜃

𝜏𝜀1𝜏𝜀2

Figure 2: Inputs and outputs of the aerial robot.

4 International Journal of Aerospace Engineering

C =100

26643775T

, ð28Þ

E =001

26643775: ð29Þ

Now f can be estimated using an additional state variable.The so-called LESO of system (25) is constructed as

_z =Az + Bu + L y − yð Þ,y = Cz,

(ð30Þ

and L is the observer gain, which is calculated by a pole place-ment method [19]:

L =l1

l2

l3

2664

3775 =

3ωo

3ωo2

ωo3

2664

3775, ð31Þ

where ωo > 0 is the observer bandwidth. As a result, zi tracksxiði = 1, 2Þ and z3 estimates f . By eliminating the effect of f ,the LADRC actively compensates for lumped disturbances inreal-time.

The control law is designed as

u = u0 − z3b0

: ð32Þ

Then, the plant in system (23) is converted into aunit double integrator, which is easily stabilized with aPD controller:

€y = f − z3 + u0 ≈ u0 = λ1 re − z1ð Þ − λ2z2, ð33Þ

where re is the referenced signal. The closed-loop transferfunction pure second order without zero is given by

G2 =λ1

s2 + λ2s + λ1: ð34Þ

Similarly, the λ1 and λ2 are calculated by a pole place-ment method, namely, λ1 = ωc

2 and λ2 = 2ωc, respectively.ωc is the control bandwidth.

The aerial robot system is constructed from the attitudeloop, position loop to manipulator loop according to thetime-scale separation principle. Each loop is controlled bythe LADRC, as shown in Figure 3.

4. Controller Analysis

4.1. Stability Analysis. In this section, the stability analysis ofLADRC will be given as follows.

Prove the tracking error is bounded. Subtracting equation(30) from (25) yields

_e =Aee + Eh, ð35Þ

where e is the so-called observer error caused by the adoptionof LESO. Ae is written as

Ae =A − LC =−3ωo 1 0−3ωo

2 0 1ωo

3 0 0

2664

3775: ð36Þ

Obviously, the LESO is bounded-input and bounded-output (BIBO) stable if the eigenvalues of the characteristicpolynomial of Ae are all in the left half plane. Besides, e isbounded for the arbitrary bound h.

Lemma 1. Suppose the LESO and the control law in equation(33) are stable, the design of LADRC yields a BIBO stableclosed-loop system.

Substituting equation (33) to (32) yields

u = 1b0

−λ1 − λ2 − 1½ �z1 − re

z2

z3

2664

3775 =Qz −

1b0

re

00

2664

3775 =Qz −G,

ð37Þ

where

Q = 1b0

−λ1 −λ2 −1½ �: ð38Þ

qr

𝜓r

𝜃r

ws

𝜏𝜃

𝜏𝜀1

𝜏𝜀2

𝜏𝜙𝜙r

𝜏𝜓

LAD

RC

+ _ LAD

RC

+ _

Aer

ial r

obot

+ _

LAD

RC

+ _

LAD

RC

Fq·qq··

Figure 3: Control structure of the aerial robot.

5International Journal of Aerospace Engineering

Equations (25) and (30) are rearranged as

_x

_z

" #=

A BQ

LC A − LC + BQ

" #x

z

" #+

−B E

−B 0

" #G

h

" #:

ð39Þ

Then, one gets

eigA BQ

LC A − LC + BQ

" # !

= eigA + BQ BQ

0 A − LC

" # !

= eig A + BQð Þ ∪ eig A − LCð Þ= root s2 + λ1s + λ2

� �∪ root s2 + 3ωos2 + 3ωos + ωo

3� �:

ð40Þ

Similarly, the control system is BIBO stable if the eigen-values of equation (40) are in the left half plane. Becausethe referenced signal re is always bounded, the only nontrivialcondition is that f is differentiable.

4.2. Parameter Tuning. In the robust controller, the parame-ters ωo,ωc, and b0 together affect the control performance. Toobtain the appropriate control parameters, parameter tuningis crucial. In this regard, the artificial intelligence algorithmmay be a useful method. Several reports about this applica-tion have been found in Refs. [27, 28]. In this paper, a famousartificial bee colony (ABC) algorithm is introduced to opti-mize the parameters in LADRC. Based on the ABC algo-rithm, a cost function capturing the performance of thecontroller is minimized over a sequence of step inputs. Animproved integral of time multiplied by absolute error(IITAE) criterion is selected as the cost function:

Fc = c1

ð∞0t e tð Þj jdt + c2

ð∞0

u tð Þð Þ2dt + c3ts + c4os, ð41Þ

where Fc denotes the cost function. jeðtÞj and uðtÞ are thetracking error and control signal in the time domain, respec-tively. ts is the settling time, os is the overshoot, and c1~c4 arethe weight coefficients.

Before the experiment, parameter tuning is conducted inthe MATLAB environment with a fixed sampling time of16 s, which is similar to the one reported in Ref. [29]. Thesimulation with 100 runs is repeated five times so as to obtainthe best result. The result of the parameter tuning is shown inFigures 4–6. With the proposed method, the optimal controlparameters can be found in a finite time.

Taking the attitude loop as an example, the response tostep inputs is plotted in Figure 7. In the loop, the mean of 0and covariance of 0.01 stochastic noises are added in theinput ports. In spite of the disturbances, all the responses ofthe attitude angles can track the referenced signal withapproximately 5 s. The simulation demonstrates the effi-

ciency of the proposed controller in attitude tacking withhigh accuracy and fast convergence rate.

Another important criterion to evaluate the suitabilityand robustness of the LADRC is to analyse the control per-formance by comparing with other controllers, such as PID.Similarly, the control parameter adjustment followed stan-dard methods for tuning the PID [30]. The result fromFigure 8 indicates that the roll angle based on LADRC hasstronger robustness with respect to disturbances than theone based on PID. Note that the attitude loop is always run-ning at a higher frequency than the position loop to guaran-tee that the Euler angles are close to zero.

In addition, the effects of wind and aerodynamics such asblade flapping as well as aerodynamic drag are neglected inhexarotor dynamics in equation (20). The detailed discus-sions about these effects on multirotors can be found inRef. [31]. The role of this simulation is to acquire a set of

2.0

1.5

xr

yr

zr

xy

z

Posit

ion

(m)

1.0

0.5

0.00 1 2 3

Time (s)

4 5

Figure 4: Response of the position loop.

2000

1800

1600

1400

1200

1000

800

Cost

func

tion

valu

e

600

400

200

00 50 100

Iteration

Figure 5: Evolving curve of the ABC algorithm.

6 International Journal of Aerospace Engineering

applicable control parameters for the following experiments.Subjected to the poor experimental condition, the wind andaerodynamics could not be measured. Hence, these factorsas well as modelling uncertainties are substituted by stochas-tic noise.

5. Experimental Validation

5.1. Experiment Setup. This section presents real-time exper-imental results obtained when applying the proposed robustcontroller for the aerial robot. Figure 9 shows the experi-mental platform designed to investigate the maneuverabilityof the aerial robot. The platform consists of a hexarotorequipped with a 2-DOF manipulator, a Futaba remote con-trol unit, a ground station, a Pixhawk controller, a globalposition system (GPS), and a couple of XBee wireless datalinks. The ground station sends a series of commands tothe aerial robot via the XBee at a frequency of 50Hz. Mean-while, it collects and saves the experimental data in real-

time. If some faults occur during the automatic control,the operator will manually manipulate the aerial robot bythe Futaba.

Tables 1 and 2 summarized the aerial robot parameters,including mass, inertia moment, and standard Denavit-Hartenberg (DH) parameters. The inertia moments are mea-sured by a two-line method, which is referred to in Ref. [32].

In the experiment, the aerial robot is driven to performthree tasks. More specifically, the tasks consist of taking off,grabbing a 0.3 kg water bottle and dropping it in the desig-nated area during flight, and landing. The planar graph ofthe experimental environment is depicted in Figure 10.

5.2. Experiment Results. With the flight path planned in theground station, the flight tasks are emulated in MATLABenvironment. Then, the control scheme, including theadjusted control parameters, is transformed to C-codes

1000

800

600

Para

met

ers

400

200

0

–2000 50

Iteration100

𝜔o-x

b0-x

𝜔c-y

𝜔o-z

b0-z

𝜔c-𝜃

𝜔o-𝜙

b0-𝜙

𝜔c-𝜓

𝜔o-𝜖

1

b0-𝜖

1

𝜔c-𝜖

2

𝜔o-y

b0-y

𝜔c-x

𝜔o-𝜃

b0-𝜃

𝜔c-z

𝜔o-𝜓

b0-𝜓

𝜔c-𝜙

𝜔o-𝜖

2

b0-𝜖

2

𝜔c-𝜖

1

Figure 6: Dynamic process of parameter tuning.

50

25

0

Atti

tude

(deg

)

–25

–500 1 2

Time (s)

𝜙r

𝜙

𝜃r

𝜃

3 4 5

Figure 7: Response of the roll angle and pitch angle.

5

PIDLADRC

0

–5

–10

0 4 8 12Time (s)

𝜙 (d

eg)

16

Figure 8: Response of the roll angle.

7International Journal of Aerospace Engineering

through the Pixhawk pilot support package (PSP) [33]. Weperform the flight experiments sixteen times, and the resultof the trials is given in Figure 11. The results show that finish-ing all the tasks has a high degree of difficulty with a barely31.25 percent success rate. The main reason is that it is diffi-cult to stabilize the attitude and position of the aerial robotduring grabbing of the bottle.

During the experiment, the flight altitude of the aerialrobot is set at 1m to reduce the effect of air as much as pos-

sible. The results are summarized in Figures 12–16. First ofall, in Figure 11, it is clear that all the tasks have been accom-plished. The snapshots in Figure 12(b)–12(d) also show theprocess of the aerial robot manipulating the bottle from thestool. At that moment, the aerial robot provides a stable atti-tude and position through the LADRC controller.

Figure 13 depicts the position tracking curves in threeaxes using the GPS sensor while flying missions. From theresults, we find that the control performance degrades signif-icantly when the manipulator moves, especially in the pro-cess of grabbing the bottle or dropping it. That may beattributed to the dynamical coupling between the hexarotorand manipulator.

Ground station

XBee

Futaba22

0 m

m

450

mm

Target object

XBee

Pixhawk

Flightcontroller

SimulinkGPS

ServoESC

Aerial robot

PC

Figure 9: Structure of the equipment platform.

Table 1: Aerial robot parameters.

Parameter Hexarotor Link 1 Link 2

m (kg) 3.64 0.164 0.409

Ixx (kg·m2) 7:2 × 10−2 1:9 × 10‐4 2:2 × 10‐4

Iyy (kg·m2) 6:9 × 10‐2 2:6 × 10‐4 1:8 × 10‐4

Izz (kg·m2) 1:1 × 10‐2 3:7 × 10‐4 1:5 × 10‐4

Table 2: Standard DH parameters of the manipulator.

Parameter Value

Link i 1 2

Link twist (deg) 90 0

Link length (mm) 50 103

Link offset (mm) 0 0

Joint angle (deg) -60~10 -90~90

Taking-offpoint

Targetobject

Landing point

Designated area

Figure 10: Sketch of experiment environment.

8 International Journal of Aerospace Engineering

To further evaluate the control performance of the posi-tion loop, root-mean-square-error (RMSE) and maximum-error (ME) values are calculated between the referencedand actual positions, which are given in Table 3. As men-tioned in Section 4, the slow position responses cause errorsto accumulate as the goal reference is reached. Nevertheless,it can be observed that the position tracking is achieved withacceptable tracking errors in the presence of external distur-bances and manipulator movement.

In addition, the other state variables of the aerial robotare displayed in Figures 14–16. Based on the proposedcontrol scheme, these system states have slight chatteringdue to measurement noise. There are some surge oscillations

(a) (d)

(b) (e)

(c) (f)

Figure 12: Snapshots of the objective operation.

16

GrabbingDropping

LandingAll tasks

14

12

10

Tria

l

8

6

4

2

0Achievement

Figure 11: Results of the trials.

50

20

x (m

)

40

60

10

Referencex

15 20 25

Manipulator movement

Time (s)30 35 40 45 50

(a) x-position

0

–1y

(m)

1

Manipulator movement

5 10 15 20 25Time (s)

30 35 40 45 50

Referencey

(b) y-position

0.5

0.0

z (m

)

1.0

Manipulator movement

5 10 15 20 25Time (s)

30 35 40 45 50

Referencez

(c) z-position

Figure 13: Position trajectories in time history.

9International Journal of Aerospace Engineering

while the end-effector grabs or drops the bottle in the timeintervals ([20, 25] and [35, 37], respectively). As a result,the change of load can affect the control performance of theposition and attitude of the aerial robot. Despite that, allthe state variables are stabilized within an acceptable limit.

It confirms the robustness of the proposed control techniquewith respect to the abrupt disturbances.

During the experiment, the variation of the two jointangles is displayed in Table 4. The trajectories in joint spaceare planned by the third-order polynomial. Polynomialfunction is simple to compute and can easily provide smoothwaypoints. The outputs of the manipulator are given inFigure 17, where the raw data can be observed by encoders.From the results, the actual responses of the joints match thereferenced trajectories well in spite of lumped disturbances

5–16

–8

0

8

16

10 15 20 25Time (s)

Atti

tude

(deg

)

30 35 40 45 50

𝜃

𝜙

𝜓

Figure 14: Attitude trajectories in time history.

5-1

0

1

2

3

4

10 15 20 25Time (s)

Line

ar v

eloc

ities

(m/s

)

30 35 40 45 50

y

x

z

.

.

.

Figure 15: Linear velocities in time history.

5–1.0

–0.5

0.0

Ang

ular

vel

ociti

es (d

eg/s

)

0.5

1.0

10

𝜃

15 20 25Time (s)

30 35 40 45 50

𝜙

𝜓

.

.

.

Figure 16: Angular velocities in time history.

Table 3: RMSE and ME of position loop.

Index x (m) y (m) z (m)

RMSE 10.155 1.575 2.471

ME 3.778 0.243 0.277

Table 4: Variation of two joint angles.

Time (s) ε1 (deg) ε2 (deg)

5 0 -30

13 -60 0

21 -60 0

27 0 -30

50 0 -30

5

0

–20

–40𝜀 1 (deg

)

–60

10 15

ReferenceActual data

20 25Time (s)

30 35 40 45 50

(a) Torque of joint 1

5 10 15 20 25Time (s)

30 35 40 45 50

0

–10

–20𝜀 2 (deg

)

–30

ReferenceActual data

(b) Torque of joint 2

Figure 17: Joints of the manipulator in time history.

10 International Journal of Aerospace Engineering

and dynamic coupling from the hexarotor. It indicates thatthe developed dynamic model can reflect the dynamicbehaviour of the aerial robot, and the proposed controllercan obtain a satisfying operating performance. However,the force applied to each joint could not be measured dueto the lack of force sensors. A satisfactory force control per-formance could be expected in practice if there are high-costsensors. This issue will be investigated in our future work.

6. Conclusion

We have presented modelling and control techniques to per-form an aerial robot using an unmanned hexarotor andmultiple-degree manipulator arms. The system model ofthe aerial robot is established by the Euler-Lagrange method,including the kinematics and dynamics. Based on the model,a robust controller using the LADRC method is presented tomanipulate the system. Moreover, the suitable control per-formance can be obtained by the ABC algorithm. Throughsome numerical simulation cases, it is demonstrated thatthe proposed controller has good robustness against para-metric uncertainties and external disturbances, compared tothe PID method. With the proposed controller, the attitudeloop, position loop, and manipulator loop are stabilized whilethe aerial robot performs the aerial tasks. The successfulexperimental results indicate that the proposed controlmethod can be a practical solution for aerial manipulation.

Data Availability

The parameters of the aerial robot we used have been shownin the paper. The data of the simulations and experimentscan be provided if necessary.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Authors’ Contributions

Li Ding, Zhenqi Gao, Ming Huang, and Hongtao Wucontributed equally to this work.

Acknowledgments

Helpful discussions with Professor Yu Yao from NanjingUniversity of Aeronautics and Astronautics on his guidancein the control theory of aerial robots are gratefully acknowl-edged. This work was partially supported by the FoundationResearch Project of Jiangsu Province (the Natural ScienceFund No. BK20170315), Changzhou Sci&Tech Program ofChina (Grant No. CJ20179017).

References

[1] M. Orsag, C. Korpela, S. Bogdan, and P. Oh, “Dexterous aerialrobots—mobile manipulation using unmanned aerial systems,”IEEE Transactions on Robotics, vol. 33, no. 6, pp. 1453–1466,2017.

[2] A. E. Jimenez-Cano, G. Heredia, M. Bejar, K. Kondak, andA. Ollero, “Modelling and control of an aerial manipulatorconsisting of an autonomous helicopter equipped with amulti-link robotic arm,” Proceedings of the Institution ofMechanical Engineers, Part G: Journal of Aerospace Engineer-ing, vol. 230, no. 10, pp. 1860–1870, 2016.

[3] E. Khanmirza, K. Daneshjou, and A. K. Ravandi, “Underactu-ated flexible aerial manipulators: a new framework for optimaltrajectory planning under constraints induced by complexdynamics,” Journal of Intelligent & Robotic Systems, vol. 92,no. 3-4, pp. 599–613, 2018.

[4] T. W. Danko and P. Y. Oh, “Design and control of a hyper-redundant manipulator for mobile manipulating unmannedaerial vehicles,” Journal of Intelligent & Robotic Systems,vol. 73, no. 1-4, pp. 709–723, 2014.

[5] K. Baizid, G. Giglio, F. Pierri et al., “Behavioral control ofunmanned aerial vehicle manipulator systems,” AutonomousRobots, vol. 41, no. 5, pp. 1203–1220, 2017.

[6] S. Kim, H. Seo, J. Shin, and H. J. Kim, “Cooperative aerialmanipulation using multirotors with multi-dof robotic arms,”IEEE/ASME Transactions on Mechatronics, vol. 23, no. 2,pp. 702–713, 2018.

[7] M. Orsag, C. M. Korpela, S. Bogdan, and P. Y. Oh, “Hybridadaptive control for aerial manipulation,” Journal of Intelligent& Robotic Systems, vol. 73, no. 1-4, pp. 693–707, 2014.

[8] P. E. Pounds and A. M. Dollar, “Aerial grasping from ahelicopter UAV platform,” in Experimental Robotics, pp. 269–283, Springer, Berlin, Heidelberg, 2014.

[9] X. Ding and S. Yu, “A multi-propeller and multi-functionaero-robot and its motion planning of leg-wall-climbing,”ActaAeronautica Et Astronautica Sinica, vol. 10, 2010.

[10] H. Abaunza, P. Castillo, A. Victorino, and R. Lozano, “Dualquaternion modeling and control of a quad-rotor aerialmanipulator,” Journal of Intelligent & Robotic Systems,vol. 88, no. 2-4, pp. 267–283, 2017.

[11] G. Mohamed, A. A. Sofiane, and L. Nicolas, “Adaptive supertwisting extended state observer based sliding mode controlfor diesel engine air path subject to matched and unmatcheddisturbance,” Mathematics and Computers in Simulation,vol. 151, pp. 111–130, 2018.

[12] K. Ryu and J. Back, “An output feedback coordinated trackingcontroller for high-order linear systems,” International Jour-nal of Control, Automation and Systems, vol. 13, no. 6,pp. 1360–1368, 2015.

[13] G. Rigatos, P. Siano, and N. Zervos, “Sensorless control of dis-tributed power generators with the derivative-free nonlinearKalman filter,” IEEE Transactions on Industrial Electronics,vol. 61, no. 11, pp. 6369–6382, 2014.

[14] F. Rinaldi, S. Chiesa, and F. Quagliotti, “Linear quadraticcontrol for quadrotors UAVs dynamics and formation flight,”Journal of Intelligent & Robotic Systems, vol. 70, no. 1-4,pp. 203–220, 2013.

[15] T. Baca, G. Loianno, and M. Saska, “Embedded model predic-tive control of unmanned micro aerial vehicles,” in 2016 21stinternational conference on methods and models in automationand robotics (MMAR), pp. 992–997, Miedzyzdroje, Poland,2016.

[16] J. Gadewadikar, F. L. Lewis, K. Subbarao, K. Peng, and B. M.Chen, “H-infinity static output-feedback control for rotor-craft,” Journal of Intelligent and Robotic Systems, vol. 54,no. 4, pp. 629–646, 2009.

11International Journal of Aerospace Engineering

[17] M.Orsag, C. Korpela, and P. Oh, “Modeling and control ofMM-UAV:mobile manipulating unmanned aerial vehicle,” Journal ofIntelligent & Robotic Systems, vol. 69, no. 1-4, pp. 227–240, 2013.

[18] S. Kim, H. Seo, S. Choi, and H. J. Kim, “Vision-guided aerialmanipulation using a multirotor with a robotic arm,”IEEE/ASME Transactions on Mechatronics, vol. 21, no. 4,pp. 1912–1923, 2016.

[19] Z. Gao, “Scaling and bandwidth-parameterization basedcontroller tuning,” in Proceedings of the 2003 AmericanControl Conference, Denver, CO, USA, USA, 2003.

[20] J. Zhang, J. Feng, Y. Zhou, F. Fang, and H. Yue, “Linear activedisturbance rejection control of waste heat recovery systemswith organic Rankine cycles,” Energies, vol. 5, no. 12,pp. 5111–5125, 2012.

[21] Y. Liu, J. Liu, and S. Zhou, “Linear active disturbance rejec-tion control for pressurized water reactor power,” Annals ofNuclear Energy, vol. 111, pp. 22–30, 2018.

[22] P. Corke, Robotics, Vision and Control: Fundamental Algo-rithms in MATLAB® Second, Completely Revised, vol. 118,Springer, 2017.

[23] Y. Sun, G. Ma, M. Liu, C. Li, and J. Liang, “Distributed finite-time coordinated control for multi-robot systems,” Transac-tions of the Institute of Measurement and Control, vol. 40,no. 9, pp. 2912–2927, 2018.

[24] L. Ding, X. Li, Q. Li, and Y. Chao, “Nonlinear friction anddynamical identification for a robot manipulator withimproved cuckoo search algorithm,” Journal of Robotics,vol. 2018, Article ID 8219123, 2018.

[25] W. Dong, G.-Y. Gu, X. Zhu, and H. Ding, “High-performancetrajectory tracking control of a quadrotor with disturbanceobserver,” Sensors and Actuators A: Physical, vol. 211,pp. 67–77, 2014.

[26] L. Ding, H. Wu, and X. Li, “Trakectory tracking congrol for anunmanned hexrotor with lumped distrubances,” Chinese Jour-nal of Engineering, vol. 40, no. 5, 628 pages, 2018.

[27] O. A. Sahed, K. Kara, A. Benyoucef, andM. L. Hadjili, “An effi-cient artificial bee colony algorithmwith application to nonlin-ear predictive control,” International Journal of GeneralSystems, vol. 45, no. 4, pp. 393–417, 2016.

[28] B. Afşar, D. Aydin, A. Uğur, and S. Korukoğlu, “Self-adaptiveand adaptive parameter control in improved artificial bee col-ony algorithm,” Informatica, vol. 28, no. 3, pp. 415–438, 2017.

[29] L. Ding, R. Ma, H. Wu, C. Feng, and Q. Li, “Yaw control of anunmanned aerial vehicle helicopter using linear active distur-bance rejection control,” Proceedings of the Institution ofMechanical Engineers, Part I: Journal of Systems and ControlEngineering, vol. 231, no. 6, pp. 427–435, 2017.

[30] Y. Nishikawa, N. Sannomiya, T. Ohta, and H. Tanaka, “Amethod for auto-tuning of PID control parameters,” Automa-tica, vol. 20, no. 3, pp. 321–332, 1984.

[31] Y. Guo, B. Jiang, and Y. Zhang, “A novel robust attitude con-trol for quadrotor aircraft subject to actuator faults and windgusts,” IEEE/CAA Journal of Automatica Sinica, vol. 5, no. 1,pp. 292–300, 2018.

[32] Y. Liu, C. Chen, H. Wu, Y. Zhang, and P. Mei, “Structural sta-bility analysis and optimization of the quadrotor unmannedaerial vehicles via the concept of Lyapunov exponents,” TheInternational Journal of Advanced Manufacturing Technology,vol. 94, no. 9-12, pp. 3217–3227, 2018.

[33] Matlab, Pixhawk Pilot Support Package (PSP) User Guide,MathWorks Pilot Engineering Group, 2017.

12 International Journal of Aerospace Engineering

International Journal of

AerospaceEngineeringHindawiwww.hindawi.com Volume 2018

RoboticsJournal of

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Shock and Vibration

Hindawiwww.hindawi.com Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwww.hindawi.com

Volume 2018

Hindawi Publishing Corporation http://www.hindawi.com Volume 2013Hindawiwww.hindawi.com

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwww.hindawi.com Volume 2018

International Journal of

RotatingMachinery

Hindawiwww.hindawi.com Volume 2018

Modelling &Simulationin EngineeringHindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Navigation and Observation

International Journal of

Hindawi

www.hindawi.com Volume 2018

Advances in

Multimedia

Submit your manuscripts atwww.hindawi.com