Mobile Manipulating Unmanned Aerial Vehicle (MM-UAV):Towards Aerial Manipulators

Matko OrsagFaculty of Electrical Engineering and Computing

University of ZagrebUnska 3

10000 Zagreb, Croatia

Abstract—This paper presents a control scheme to achieve dynamic stability in an aerial vehicle with dual multi-degree of freedommanipulators. Arm movements assist with stability and recovery for ground robots, in particular humanoids and dynamically balancingvehicles. However, there is little work in aerial robotics where the manipulators themselves facilitate flight stability or the load mass isrepositioned in flight for added control. We present recent results in arm motions that achieve increased flight stability without and withdifferent load masses attached to the end-effectors. Our test flight results indicate that we can accurately model and control our aerialvehicle when both moving the manipulators and interacting with target objects.

Index Terms—UAV, Dexterours manipulation, Stability.

F

1 INTRODUCTION

Historically, UAV research has been focused on avoidinginteraction with the environment. This fact is mostly dueto poor payload capabilities available in micro UAVs inaddition to the possibility of crashing and causing injury.So far, UAVs have been used mostly in surveillance andsearch and rescue missions [1]–[4].

However, the ability for air vehicles to manipulatea target or carry objects they encounter could greatlyexpand the types of missions achievable by unmannedsystems. Flying robots with dexterous arms could lead totransformative applications in near-Earth environments.Such applications could be infrastructure inspection andrepair, agricultural care and possibly even constructionand assembly. The authors envision a paradigm shift inthe way UAVs are currently deployed (Fig. 1).

Although work has been done in this area withground-based vehicles, little work has been done inaerial vehicles where arm or manipulator motions maylead to decreased stability and control problems. Re-

Fig. 1: MM-UAV carrying a long rod

cently, there have been a few successful attempts in aerialgrasping using a 1-DOF (degree of freedom) grasperor gripper [5], [6], [7]. Other groups have introducedgimbals [8], suspended payload [9], force sensors [10], orbrushes [11] attached to quadrotors or duct-fan vehicleswhere the manipulator is used for contact inspection.The AIRobots consortium [12] is also developing servicerobots for use in hazardous or unreachable locations.Previous work from the authors has produced a proto-type 3-arm aerial manipulator in addition to a miniaturegantry based test and evaluation quadrotor emulationsystem [13], [14].

While mobile manipulation continues to be a highlyactive field of study, much of the focus so far lies withground vehicles. In recent years, robots that rely on dy-namic control techniques for movement or manipulationhave become increasingly prevalent. Robotic systems ofthis type involve challenging control problems due inpart to the fact that a robot’s base and it’s manipulatorsmay be dynamically coupled. For dynamically balanc-ing robots, robots with flexible bases, or humanoids,base reactions created by the vehicle’s manipulator maybe significant enough to warrant active reduction orcompensation to maintain stability. Previous work withground systems has shown that if vibration suppressioncontrol is not correctly handled it can lead to destabiliz-ing effects [15]. Additionally, others have analyzed armrecovery motions to reduce the impact on a dynamicallystable base vehicle [16]. Similar work with humanoidshas been done involving balancing during manipulationor grasping for added stability [17]. It is apparent thatcompensation of reactionary forces caused during ma-nipulation or manipulator movement is critical to robustcontrol of an aerial vehicle. Reaction forces observed dur-ing arm movement and those caused by ground contact

introduce destabilizing effects into an already inherentlyunstable system. Novel control architectures for flightand arm dynamics are required to maintain stability dur-ing manipulation and flight. However, aerial graspingand manipulation still remains largely underdeveloped.This fact is mostly due to poor payload capabilitiesavailable from micro UAVs in addition to the possibilityof crashing and causing injury. This work tries to expandthe current state of the art by investigating underlyingdynamics of a quadrotor with two 4DOF manipulators.The paper is organized as follows: Current state of the artin aerial manipulation is presented first; following witha brief kinematic and dynamic analysis of MM-UAV;Stability of a simple PID attitude controller is analyzednext; finally simulation model and simulation results arepresented and discussed in the last two paragraphs.

2 STATE OF THE ART IN AERIAL MANIPULA-TION

Current State of the art in Aerial manipulation hasfocused mostly on single DOF gripper manipulatorsand slung load transport. A lot of researchers that con-tributed to this field of aerial robotics have so far focusedon 3 key aspects:

• Contact inspection (Pose/Wrench control) Fig.2• Slung load transport Fig. 3• Single Degree of freedom grippers Fig.4

2.1 Pose/Wrench controlIn [10], authors introduced wrench control to give thequadrotor an ability of stable motion while in contact.The authors used a hybrid Pose/Wrench framework ca-pable of switching between pure Pose and Pose/Wrenchcontrol but the operator is required to make the switch.Instead of using additional force/torque sensors, authorsutilized a wrench estimator using quadrotor inputs andpose measurements. Another hybrid Force/Position con-trol concept based on state feedback is introduced in [18],[19]. In this work, a duct-fan aerial vehicle is used toachieve contact inspection tasks. The authors presented amechanical design to cope with inherent zero dynamicsof the system. The authors in [20] also researched theproblem of UAV rotorcraft in compliant contact.

2.2 Slung LoadAuthors in [21] explored the possibility of using singleand multiple UAVs to assist in search and rescue (SAR)missions. They tested formations of up to three small sizepetrol powered helicopters that cooperatively transporta slung load. The authors were capable of transporting avideo camera with three small size helicopters in adverseweather conditions that exhibited high wind speeds ofup to 35km/h. A group of authors in [22] implementedan additional vision system that measured the positionof the slung load. They proposed an adaptive controllerthat reduced the swing in the load. In order to solve a

(a) The quadrotor executes a controlled force of 3N in the x-direction of f, while simultaneously moving up and down alongthe plate [10].

(b) Ducted fan prototype, equipped with nondestructive testingdevices, inspects by contact a structure to detect possible cracksor small defects [18].

Fig. 2: Contact inspection (Pose/Wrench control)

similar problem with quadrotors carrying a slung load,authors in [9] proposed a technique based on dynamicprogramming which ensured swing free trajectory track-ing.

In [23], a tethered helicopter configuration is modeledand tested. This configuration proved to be more stablein presence of disturbances (i.e. wind gusts) then anon-tethered helicopter. Tether also introduced coupleddynamics, adding to the complexity of the overall con-troller. Nevertheless, tether is a very interesting conceptthat could potentially be used in twofold manner: Itcould provide unlimited supply of electricity; It couldalso be used as additional pose and position measure-ment system.

2.3 Single DOF GrippersThe authors in [6], [24], [25] analyzed the stability of ahelicopter and a quadrotor with added payload mass.Using Routh-Hourwitz criteria, the authors derived aconnection between the mass off the added payload,its offset from UAV center of mass and the stability of

(a) Swing-free trajectory tracking of a quadrotor with suspendedload. [9].

(b) Three UAVs transporting a pan-tilt wireless camera [21].

Fig. 3: Slung load transport

the UAV. Plotting offset vs. mass stability regions, theyclearly showed how a bigger mass tightens the stabilityregion of the aircraft. Namely, the bigger the mass, thesmaller the available offset region, so that the vehiclehas to grab the additional payload as close to the centerof gravity as possible. Quadrotor stability in presenceof unknown payload disturbances was discussed in [5].Here the authors look into the possibility of estimatingdisturbance parameters (i.e. mass and moments of iner-tia). Using hover mode to estimate the parameters, theyeffectively eliminated the Euler angles and the deriva-tives of the position from the equations. This researchgroup also contributed by doing an experimental studywith teams of quadrotors cooperatively grasping, stabi-lizing, and transporting payloads along desired three-dimensional trajectories [26]. They went a step furtherand showed the experimental results of team of quadro-tors performing automated assembly of Special Cubictype Structures [27]. They used their gripping tool topick up the simple structural nodes and used magneticendings on the structures to piece them together.

2.4 Beyond the current State of the ArtThe aim of this research is to extend the current stateof the art by introducing multiple degree of freedom

(a) Yale Aerial Manipulator carrying a 1.5 kg toolcase in hover[25].

(b) Four quadrotors carrying a payload in the El configuration.[26].

Fig. 4: Air robots with 1DOF grippers

manipulators. To the extent of authors knowledge, littleor no attempt has been made to implement such anaerial vehicle so far. Afore mentioned state of the artis limited to simple manipulation problems (i.e. Pickand place, contact inspection, painting, etc.). Multiple -Degree of Freedom manipulators expand the capabilitiesof aerial robots by giving them the ability to: Perch andmanipulate, Twist valves on or off, Assemble objects,remove obstacles and many other.

Introducing multiple degrees of freedom adds to thecomplexity of the control problem. Therefore, the firstgoal of this research is to achieve and sustain a stableflight while moving manipulator arms. A lot of researchin mobile robotics as well as the research in air robotswith 1DOF grippers can be utilized to solve this problem.After this, next research step would be to implementcurrent state of the art in contact stability and loadestimation which would yield a fully dexterous aerialrobot. The following two chapters present a first steptowards a fully dexterous MM-UAV.

3 MM-UAV DYNAMIC MODEL

In order to stabilize a MM-UAV, one needs to devise itsdynamic model first. The dynamics of quadrotors arewell understood [28]–[30] but there is a critical gap inapplying mobile manipulation to air vehicles. Dexterousmobile manipulators have already been successfully de-ployed and researched on both autonomous underwater

Link θ d a αB-0 π

2db ab 0

0 0 0 0 01 q1A − π

20 3.75 −π

22 q2A 0 3.75 π

23 q3A 0 3.75 −π

24 q4A + π

20 0 π

2T-E 0 0 3.75 0

TABLE 1: DH Parameters for Manipulators [cm] (Arm Aonly).

vehicles, spacecrafts and mobile robots [31], [32], [33],[34]. Therefore, various mathematical formalisms fordynamic modeling that have already been tested for thisclass of vehicles can be adapted for UAVs. This paperaims to further develop a 1st generation 3 Arm MM-UAV prototype [13]. While we gained critical knowledgefrom the 1st generation prototype its 2 DOF manipula-tors still lacked the desired dexterity. Therefore, in thischapter we propose a 2nd generation MM-UAV that has2 manipulators, each having 4 degrees of freedom (Fig.5).

3.1 Manipulator KinematicsForward kinematics for the two serial chain manipula-tors are derived using Denavit-Hartenberg (DH) param-eters as shown in Table 1. Parameters θ, d, a, and αare in standard DH convention and q1i , q2i , q3i , and q4iare joint variables of each manipulator arm i = [A,B].Both arms are symmetrical and offset equally from thevehicle’s geometric center. Since the general kinematicstructure is identical for the right and left arms, thecoordinate frames are the same for each arm, only thelink B-0 is different. Reference frames are shown inFig. 5 which relate the inertial or world frame, W , tothe vehicle or body frame, B, to the tool or end-effectorframe, E. To make the DH parameters consistent, anadditional frame is set in the origin of frame L4. Thedirect kinematics function relating the quadrotor body tothe end-effector frame is obtained by chain-multiplyingthe transformation matrices together.

3.2 Manipulator DynamicsUsing the recursive Newton-Euler approach, each armis modeled as a serial chain RRRR manipulator. Thequadrotor body frame is first modeled as a static revolutejoint with a constant angular offset for each MM-UAVarm (Link B-0). Equations can easily be augmentedto account for the mobile base by adding quadrotordynamics to the base frame [35]. In this paper, forcesand torques are viewed from the quadrotor body framein which the low level attitude controller stabilizes theaircraft [13].

With Denavit-Hartenberg parameterization, jointframes are set and direct kinematics equations for eachserial chain are derived. This procedure is repeated forboth manipulator arms. Given the initial angular ΩB

Bz

By

Bx

10 , yy

10 , xx

10 , zz

2y 2z

2x

3z

3x

3y

4z

4x 4yTxTz

Ty

Ez ExEy

Body

WyWorld

Wx

Wz

Fig. 5: Reference Frames for Manipulator Arms

and translational VB velocities of the quadrotor body,the angular ~ωij and translational ~vij velocities and thederivatives of the velocity vectors (i.e. vij and ωij) foreach joint j and each arm i, can be propagated andexpressed in the quadrotor body frame. After forwardstep calculations of joint speeds and accelerations,applying Newton-Euler laws obtains the necessary forceand torque equations.

3.3 Quadrotor Dynamics

The focus of this paper is to show how manipulatordynamics influence the dynamics of the quadrotor. Assuch, quadrotor dynamics considered in this paper donot account for various aerodynamic effects (i.e. bladeflapping, ground effect, etc.) experienced during highlydynamic flying maneuvers. Most of the vehicle’s criticalmotions occur around hover outside of ground effect.This fact justifies a simplified mathematical model sincewith given speeds and maneuverability, the quadrotorexperiences little to none of the previously mentionedaerodynamic effects.

The quadrotor dynamic model begins with Newton-Euler equations for rigid body translation and rotation[36]. Because the mobile manipulator dynamics are in-troduced through the recursive Newton-Euler method, itis possible to consider the quadrotor motion as separatefrom the manipulator. Manipulator mass, moments ofinertia, and movement are later calculated and regardedas disturbances to the quadrotor model.[

Fqτq

]=

[mqI 0

0 Jq

] [~v~ω

]+

[0

~ωq × Jq~ωq

](1)

The second key part of quadrotor dynamics is thepropulsion system torque and thrust. With no additionalaerodynamic effects, propeller thrust and drag can be es-timated using the NACA-standardized thrust and torquecoefficients CT (2a) and CQ (2b). In [37], the authorsmeasured the performance of various propellers used

in UAVs. Knowing the thrust and torque coefficients ofgiven propellers, one can easily calculate the thrust andtorque of each propeller with respect to applied voltage.

CT =T

ρn2D4(2a)

CQ =Q

ρn2D5(2b)

Rotor thrust and torque are marked T and Q, re-spectively; ρ stands for air density which is assumedto be constant; n ∝ U [V ] is the rotor speed; and D isthe rotor radius. Forces and torques of each propellerare added according to standard quadrotor propulsionsystem equations as shown in (3).

~Ftot = ~T 1 + ~T 2 + ~T 3 + ~T 4

τ totx = τ2x + τ3x − τ1x − τ4xτ toty = τ3y + τ4y − τ1y − τ2yτ totz = τ2z + τ4z − τ1z − τ3z

(3)

Dynamics of brushless DC motors used on the aircraftproved to have an important impact in aircraft stabilityand cannot be omitted from the MM-UAV model. Off theshelf electronic speed controllers are used to power andcontrol the motors, which makes it impossible to devisea complete model for the motors. Therefore, a simplified1st order PT1 dynamic model is used.

Considering simplified aerodynamic conditions, pro-pellers simply produce thrust forces T i as shown in (2a).Summing them all together gives the total aircraft thrust.Each propeller torque τ i, in contrast, has two compo-nents, one coming from the actual propeller drag (2b),and the other due to the displacement of the propellerfrom the COG.

~τ i = ~Qi + ∆~RiT × ~T i (4)

4 STABILITY ANALYSIS

Given the dynamic model for both manipulators and thequadrotor body, a simplified arm model is utilized toestablish stability criteria for the complete system. Muchof the previous work in quadrotor flight and stabilityassumes the geometric center and quadrotor center ofmass are coincident. In our model as shown in Figs.6a and 6b, the quadrotor center of mass QCM is shownoffset downward in the z direction due to the mass ofthe arms. Further, the overall center of mass, CM , shiftsbased on the joint angles of the two shoulder joints.

Previous work in aircraft stability analysis has mea-sured center of mass offsets based on the load mass whileignoring affects from the gripper [5], [6]. In this work,the 4-DOF arms and end-effectors introduce a significantincrease in payload and disturbance to the dynamics andtherefore cannot be neglected.

4.1 Angle Control StabilityControl of the MM-UAV body is achieved through PI-Dcontrol shown in Fig. 7. This form of PID control waschosen because it eliminates potential damages to theactuators that can usually be experienced when leadingthe control difference directly through the derivationchannel [38]. In order to analyze the stability of thesystem, one needs to know the varying parameters inthe control loop. The disturbance caused from the Eulerequation component ωyωz(Iyy− Izz) affects the behaviorof the control loop, but not its stability and therefore willnot be considered in this analysis. The major factor thataffects the stability of the aircraft is the moment of inertiaJ = Ixx, Iyy. Mathematical formalisms that describe thevariations in the moment of inertia were given in Sec. 3.2.

The transfer functions of the angle control loop in Fig.7 can easily be derived (5). Similarly as in [6], the stabilityconditions are applied to its 4th order characteristicpolynomial a4s4 + a3s

3 + a2s2 + a1s+ a0, where the 4th

order dynamic system includes both the dynamics of theaircraft and motor dynamics.

GαCL=

KDKm

KiTmJ

(Kp

Kis+ 1

)s4 + 1

Tms3 + KDKm

TmJs2 +

KdKmKp

TmJs+ KdKmKi

TmJ(5)

Coefficients KD, Kp and Ki are PI-D respective gains andKm and Tm represent propulsion system gain and motortime constant. If we apply the Routh-Hurwitz stabilitycriteria, it is possible to derive the analytical equationsfor stability conditions. The necessary system stabilityconditions require that all coefficients be positive andthat inequalities in (6) are satisfied. Stability criteria (6)shows that, due to the dynamics introduced from themotors (i.e. Tm), the proportional control Kp can drivethe system unstable. In fact, only the derivative controlKd has the sole purpose of stabilizing the system. Thisshows how the motor dynamics cannot be neglectedwhen analyzing MM-UAV stability.

KdKmKp

Ki(1− TmKp) > J (6a)

KdKm (1− TmKp) > 0 (6b)

Moreover, the angle control loop in Fig. 7 can be ob-served as a cascade system, where the KD gain servesas inner loop controller. This approach enables tuningthe PI-D controller in two separate steps (i.e. rotationspeed and angle loop). After closing the speed loop, theinner loop transfer function takes the standard 2nd ordertransfer function form:

GωCL=

1

1 + JKDKm

s+ JTm

KDKms2

(7)

It can further be shown that the equations for the sys-tem’s natural frequency ωn and damping ratio ζ are:

ωn =

√KDKm

JTm(8a)

X

Z

GC

Qcm

Acm

CM

Bcm

GC – Geometric Center of Mass

Qcm – Quadrotor Center of Mass

CM – Center of Mass

Acm – Arm A Center of Mass

Bcm – Arm B Center of Mass

2D

R

qA

qB

ωx

ωy

L1

C1

ΔBcm

ΔAcm

ΔQcm

(a) Moving joint 1 (arms A and B), other joints remain fixed.

Y

Z

GC

Qcm

R

qA

ωy

L

Bcm

Acm

X

CM

d

DcmqB

Ls

ωx

C

(b) Simple task of picking up a box type object (Moving joints2, arms A and B)

Fig. 6: Simplified Arm Kinematics Model

++ +sT

K

m

m

1 J

1

s

1

s

1DK

sKK iP

1

PI-D

Linearized Motor

Transfer Function

zyzzyy II Static and Dynamic

Arm torques

A/D

D/A11.7V

Fig. 7: Joint Angle Control

ζ =1

2

√J

KDKmTm(8b)

While from (6) follows that a smaller moment of iner-tia increases the system stability, (8) shows that smallermoments of inertia cause oscillations in the inner loop.While that is not a problem in this analysis, in theactual implementation, where a discrete form and inputlimits are used, the amplitude and frequency of theseoscillations can cause serious problems and stabilityissues. The amplitude can causes problems when facedwith control inputs limits (i.e. 12V ) and the frequency isof concern when it surpasses the sampling frequencies.Smaller moments of inertia produce higher frequenciesand smaller damping ratios thus can decrease the stabil-ity in multiple ways.

5 SIMULATION

The simulation model for MM-UAV must incorporatequadrotor dynamics and propeller aerodynamics fromSec. 3.3, together with a complete dynamic model ofthe arms (Sec. 3.2), controlling the system with a PI-D

controller from Sec. 4. Figure 9 shows the layout forthe simulation model used in this paper. The attitudecontroller takes angle reference values and quadrotorfeedback signals as input. A PI-D algorithm then calcu-lates the necessary rotor speeds that power the propellerdynamics block that produces respective torques andforces applied to the body. A recursive Newton-Euler dy-namic model is used to model the arms as a disturbanceto the quadrotor control loop. This recursive modelcalculates the torques and forces based on movementsof the arms and quadrotor dynamics. Arm movement ismodeled through a PT2 dynamic system, tuned with thetechnical optimum criteria, that emulates expected servomotor dynamics. Matlab was used for simulations anda recursive Newton-Euler dynamics model of the ma-nipulators was implemented using the Robotics Toolbox[39].

In order to test the proposed stability analysis, a seriesof simulation tests were run. Figures 8a and 8b show theresults of one of these tests. In this particular test, thequadrotor roll controller was tuned close to the stability

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4Z

[m

]

0 2 4 6 8 10 12 14 16 18 20−10

−5

0

5

10

Θ [

° ]

0 2 4 6 8 10 12 14 16 18 20−5

0

5

Ψ [

° ]

time [s]

(a) Matlab Simulation (Take off with arms stowed , Oscillationssettled ; Deploying arms move): Roll and pitch angles

0 2 4 6 8 10 12 14 16 18 20−20

−15

−10

−5

0

Fz [

N]

0 2 4 6 8 10 12 14 16 18 20−0.4

−0.2

0

0.2

0.4

Mx, M

y [N

m2 ]

time [s]

Mx

My

(b) Matlab Simulation (Take off with arms stowed , Oscillationssettled ; Deploying arms move): Propulsion system thrust and

torque values

Fig. 8: Simulation Results

Quadrotor

ModelMotor

Dynamics

Attitude

Control

+

+

Servo

Controller

Dynamics

RRR ,,

]4:1[

Aq

]4:1[

Bq

AAA qqq ,,

BBB qqq ,,

BA,F

BA,τ

21,

43,

QQQ a

,,

QQQ a

,,

Recursive

Newton-Euler

Model

PF

Pτ

Fig. 9: Simulation Scheme

boundary. The aircraft takes off with arms tucked andstowed. After the vehicles settles to a hover, the arms aredeployed down and fully extended, thus increasing themoments of inertia. This movement causes the roll anglecontrol to become unstable, which can be seen in thered portion of Fig. 8a. The pitch controller, on the otherhand, is tuned closer to the safe, stable controller region,and thus does not become unstable. It does, however,exhibit more oscillatory behavior, due to the increase ofits moment of inertia.

Figure 8b shows the rotors forces and torques fromthis experiment. It is interesting to notice how the con-troller compensates for the additional torque load atthe beginning of the experiment. This load is causedby the arms’ center of mass positioned away from theQCM . This causes static torque on the quadrotor body,which the integral component of the PI-D controllercompensates. Once the arms are extended downward,this torque disappears as the arms’ center of mass are

closer to QCM .

6 CONCLUSION

In this paper a multi-arm manipulating aerial vehicleusing a small, off-the-shelf quadrotor that extend thecurrent state of the art in aerial manipulation is pre-sented. One of the goals of this research is to furtherpush the field of UAV research towards aerial mobilemanipulation that would yield a fully dexterous airrobot. While current state of the art is limited to simplemanipulation problems, Multiple - Degree of Freedommanipulators would significantly expand the capabilitiesof aerial robots.

The first steps towards fully autonomous dexterousMM-UAV are the system kinematics and dynamics pre-sented in this paper. Furthermore, the paper shows howthis can be applied to a PI-D controller implementationto compensate for reactionary forces during arm move-ment. Through stability analysis, the paper identifiesmanipulator joint positions that ensure flight stabilityfor a simple PI-D controller. Simulation results confirmthe kinematic and dynamic model and controller for thesystem.

In the future, the goal of this research is to testdifferent adaptive and robust control techniques in or-der to achieve greater flight stability, which would inturn enable dexterous manipulation while in flight orhovering.

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