Content uploaded by Abdullah Mohiuddin

Author content

All content in this area was uploaded by Abdullah Mohiuddin on Apr 14, 2020

Content may be subject to copyright.

Energy distribution in Dual-UAV collaborative

transportation through load sharing

Abdullah Mohiuddin∗

Khalifa University

abdullah.mohiuddin@ku.ac.ae

Randa Almadhoun

Khalifa University

UAE, Abu Dhabi

randa.almadhoun@ku.ac.ae

Yahya Zweiri

KUCARS,

Khalifa University of Science and Technology,

P.O. Box 127788, Abu Dhabi, UAE

Faculty of Science,

Engineering and Computing

Kingston University London

London SW15 3DW, UK

yahya.zweiri@ku.ac.ae

Tarek Taha

Algorythma’s Autonomous Aerial Lab

UAE, Abu Dhabi

tarek.taha@algorythma.com

Dongming Gan

School of Engineering Technology ,

Purdue University,

401 N Grant Street, West Lafayette, IN 47907, USA

dgan@purdue.edu

ABSTRACT

In this paper, a novel dual-UAV collaborative aerial transport strategy based on energy distribution and load

sharing is proposed. This paper presents the ﬁrst experimental demonstration of dual-UAV collaborative aerial

transport while distributing power consumption. The demonstration is performed while distributing the power

consumption between two drones sharing a load based on their battery state of charge. A numerical model of the

dual-hex-rotor-payload is used to validate the proposed strategy. Numerical and hardware tests were conducted

to demonstrate the load distribution using multiple UAV with certain spatial conﬁgurations. Finally, collaborative

aerial transport test scenarios are performed numerically and experimentally. The simulation and experimental

results show the effectiveness and applicability of the proposed strategy.

1 Introduction

Aerial transportation of payloads via Unmanned Aerial Vehicles (UAVs) is not a new concept [1]. A commercial online

shop and delivery company 1is currently evaluating the possible usage of aerial vehicles to deliver goods. A recent study

showed that UAV delivery might even help in the reduction of green house emissions caused by freight industry [2]. The

limitation of payload carrying capability of a single UAV can be offset by the use of multiple UAVs.

Various multi-UAV collaborative aerial transport work is present in literature providing several demonstrations of col-

laborative transport as discussed in [3–6]. These studies are focused on the collaboration of multiple UAVs, by either using

co-ordinated motion strategies [5–7] or the leader follower approaches [8, 9]. Path planning and co-operative localization

while transporting a payload using multiple UAVs were presented in [10, 11]. In [12, 13], haptic feedback based tele-

manipulation were proposed, the UAVs were equipped with 1DoF arm that could apply one point contact force to lift an

∗Corresponding author: Mohiuddin, JMR-19-1378

1https://www.thenational.ae/business/technology/ups-drone-delivery-subsidiary-seeks-new-horizons-1.891693

1

object. The studies mentioned above focus on the collaborative aerial manipulation without taking orientation of the payload

into consideration and its effect on energy distribution between UAVs.

Several papers tackled the challenge of adjusting position and orientations of the payload in mid air [14–18], however,

the uneven thrust requirements and the corresponding power distribution were not considered. In general, the orientation of

the payload and the trajectory depends on the position control of the UAVs. The work presented in [19] presented a leader

follower approach to achieve the desired pose without communication between UAVs by using non-zero internal force. In [7]

modeling of re-conﬁgurable cable-driven parallel robots (RCDPR) was used to ﬁnd the relationships between the motion of

quadrotors and the motion of a payload. These studies are not focused on the effects of the payload shape on the energy

distribution during collaborative transport [14–18].

Researchers have focused on collaborative transport of payloads with various shapes such as point mass, rectangular

blocks and deformable linear objects [20], [21]. A point mass payload requires separation between the UAVs using longer

cables as a result, the UAVs experience a pull towards each other [21]. An increase in the volume of the payload can relieve

the necessity of that pulling force. However, an increase in the volume of the payload increases the implication of the center

of gravity of the payload while distributing the thrust requirements. Most of the studies [5, 8, 9, 11] for collaborative transport

use objects of smaller width and larger length (i.e., higher aspect ratios). In case of lower aspect ratio payload, any difference

in altitude of the collaborating UAVs leads to an uneven thrust requirement, thus causing uneven energy distribution.

The thrust distribution during collaborative transport is discussed in [20,22]. The mechanism proposed by [22] regulates

the thrust requirements for transporting a point mass. This regulation, however, should be performed taking the energy

availability of the UAVs into consideration. The work presented in [20] discussed the need of equal load distribution while

transporting deformable linear objects (DLOs), the conﬁguration of multiple UAVs which can provide equal-load distribution

was estimated using particle swarm optimization (PSO). In that case, however, it is assumed that all UAVs are identical and

their battery capacities are also equivalent. The methods presented in [20, 22] were not experimentally tested for veriﬁcation.

The studies [20, 22] were also not focused on the rectangular shaped payload for thrust distribution. This study therefore

focused on the rectangular shaped payload to distribute the thrust during collaborative transport to distribute the energy

consumption.

Energy distribution management in multi-UAV collaborative transport is important since multi-rotors UAVs are known

for low ﬂight endurance [23] and power failure in one of the UAVs can make the transportation operation fail. This paper

therefore proposes a novel experimentally veriﬁed strategy to distribute the lifting load of the jointly carried object by

changing the orientation of the payload. Distribution of lifting force also enables us to regulate the power distribution

between the UAVs. This distribution of power consumption can ensure mission completion when one UAV has less state of

charge than the other.

The paper is structured as follows, Section 2 describes the generalized energy aware collaboration strategy for arbitrary

shaped paylaod carried by nUAVs. Section 2 also includes the assumptions used in this study, the multi-UAV-payload model

used for the assesment and validation of the proposed strategy, the power consumption model used. Section 3 is focused

on the application of energy distribution strategy for a 2D object along with the load sharing strategy, constraints and the

description of dual UAV collaborative transport method. Section 4 shows the simulated results while Section 5 shows the

experimental method and results.

2 General energy aware collaboration strategy

A general strategy for load distribution is devised for n=2,3 number of drones, and an arbitrary voluminous payload.

It is not possible to ﬁnd a closed form solution for load distribution when attitude angles of the payload are given. However,

assuming the payload geometry is known, it is possible to iteratively ﬁnd the required payload orientation to satisfy the

load distribution requirements, subject to geometric and equilibrium constraints. The iterative strategy would require the

information of the required power distribution ratio. The attitude angle of the payload around x-axis, and y-axis, will

incrementally increase. After each increment the force distribution ratio will be calculated, which will be used to calculate

the power distribution ratio. If the resulting power distribution ratio will be similar to the required power distribution ratio,

the iterations will stop. The process is also explained in Algorithm 1.

Let aibe the position vectors of the anchor points of the cable on the payload in the world frame εx0,y0,z0,ribe the center

of mass in the world frame εx0,y0,z0, let ˜

ribe the position vector of center of mass in body frame B˜x,˜y,˜z, and ˜

aibe the anchor

points in the body frame B˜x,˜y,˜zas shown in Figure 1. Let Rbe the rotation matrix determined by the Euler angles of the

payload κ

κ

κ= [α,β,γ]T. Given the ri,˜

aiand the attitude angles of the payload, it is possible to ﬁnd aiusing the relation

ai=r+R(˜

ai−˜

ri). Starting from an arbitrary attitude angle, the world frame location of the anchor points is found. The lift

forces fiat each anchor point in vertical axis are found using the anchor point position ai, equilibrium conditions of moments

around x and y axis, and equilibrium of forces in vertical axis. During hovering condition, the thrust u1ican be written in

the following form fi+wi=u1iwhere wiis the weight of the drone i, and fiis the lift force applied to payload by drone i.

This equation is simply showing that the combined thrust applied by the rotors of each UAV must be enough to support the

UAV‘s weight and the lifting force applied to the payload by the UAV. After calculating the resulting thrust u1iwe can use

2

Fig. 1. Payload with respect to body and world frame along with anchor points

Eq. 7 for the calculation of the required power pifor each drone. The resulting power ratios, are compared with the required

power ratios. The process is repeated till the payload attitude angles are found for which required power ratio is achieved.

However, when i=2, another method can be used to distribute the load, which is explained in Algorithm 2.

Algorithm 1: Reference load attitude generation for load distribution strategy

Input : r,ai,mp,wi,pi

Output: α,β

U pdat e→α,β;

f ind→ai;

Momentequilibrium→fi;

fi→u1i;

u1i→pi;

Check→pi;

if pi=achieved then

return;

else

Goto U pd ate

end

Return →α,β;

The above strategy is tested for lift load distribution, on a voluminous 3D object of mass 1 Kg carried by 3 UAVs. The

center of mass is assumed to be same as geometric center located at [0,0,0.5] with respect to body frame, while the anchor

points in body frame are deﬁned as [-1,0,1],[-1 0 1],[0 1.7321 1]. Algorithm 1 was tested with several lift load ratios which

it was able to process in less than 6 ms. Lower computational costs mean that there is a possibility to incorporate the strategy

for real-time implementation of the algorithm if the power consumption measurement is available in realtime. The sample

runs of the code are shown in Table 1. Algorithm 1 provided not only the required attitude angles of the payload, but also

the required position of the anchor points in world frame to achieve required load distribution.

2.1 Assumptions

Several assumptions are used for the development and testing of the strategy, which are discussed in this section.

1. We assume that the attitude dynamics of the hex-rotors is decoupled from the payload. In experiments, this is valid via

3

Table 1. Payload attitude angles for lift load distribution

Load ratio computation time (ms) α β

0.25,0.25,0.5 0.03 28.64◦-28.64◦

0.33,0.2,0.46 0.012 -25.78◦-60.16◦

0.3,0.3,0.4 0.005 -85.94◦-11.45◦

using a small cable between the metallic strip and the supporting rod of the payload. The UAV models were simpliﬁed

by assuming that the UAV structure is rigid and both Center of gravity (CoG) and geometric center are at origin U˜a,˜

b,˜c

of body frame of the UAV.

2. All aerodynamic disturbances including the lateral drag on the whole system, the thrust shielding of the payload, are

ignored. A rectangular shaped payload can result in unwanted moments caused by the downwash of the air from the

rotors. This aerodynamic inﬂuence of the payload to hex-rotors are ignored in simulations and was bypassed in hardware

experiments via selecting an equivalent payload. The equivalent payload consists of less surface area but similar relative

location of center of gravity (CoG) from the anchor points.

3. When a point mass or low volume payload is jointly carried by two or more UAVs using cables, the UAVs experience a

pull towards each other [21]. When a voluminous payload is considered with longer lengths, UAVs do not have to apply

lateral forces to stay apart from each other. This also implies that the cable direction are both along the gravity direction

as described in Eq. 3.

4. Propulsion system efﬁciency degradation during ﬂight due to voltage supply decline is ignored. We ignore battery fail-

safe activation due to voltage threshold, to achieve this, experiments are performed within limits of fail-safe activation.

5. We assume equal load sharing for lateral transportation, however the lifting load is distributed amongst UAVs via our

strategy. This is achieved by employing a collaborative transport strategy which works by moving the UAVs in synchro-

nization.

2.2 Multi-hex-rotor-payload system model

The system consists of nhex-rotors drone01, drone02... drone-n which will be from now on referred as i=1,2...n,

attached to a payload as shown in Fig. 1. Let pi= [xi,yi,zi]Tbe the position vector of the center of mass of the hex-rotor i

relative to the ﬁxed inertial frame or world frame εx0,y0,z0. The orientation of the hex-rotor iis expressed in Euler angles as

Φ

Φ

Φi= [θi,φi,ψi]Twhere θiis the roll angle about the y-axis, φiis the pitch angle about the x-axis, and ψiis the yaw angle

about the z-axis of the hex-rotor drone i. Six rotors attached to identical brush-less DC motors are rotating with a speed ωiN .

The following equations best describe the translational and rotational dynamics model used in this paper for the hex-rotor

UAVs which were modiﬁed from [24]. The model from [24] is modiﬁed to include lift forces fiin vertical axis. Furthermore,

the payload mass was equally shared by nUAVs in lateral transport direction.

(mi+n−1mp)¨xi= (sinφisinψi+cosφicosψisinθi)u1i(1)

(mi+n−1mp)¨yi= (cosφisinθisinψi−cosψisinφi)u1i(2)

mi¨zi= (cosθicosφi)u1i−wi−fi(3)

Iix ¨

φ= (Iiy −Iiz)˙

θi˙

ψi+u2i−J˙

θiu5i(4)

Iiy ¨

θi= (Iiz −Iix)˙

φi˙

ψi+u3i−J˙

φiu5i(5)

Iiz ¨

ψi= (Iix −Iiy)˙

φi˙

θi+u4i(6)

Where irepresents drone number. miis the mass of the hex-rotor UAV and mpis the mass of the jointly carried payload, and

¨xi, ¨yi, ¨ziare the translational accelerations of the hex-rotor UAV in x0,y0and z0axes. u1iis the sum of thrust TiN produced by

all motors which is calculated as ∑N=6

1TiN,u2iis the moment created by the thrust force around x-axis, u3iis the moment

created by the thrust force around y-axis and u4iis the moment created by thrust force around z-axis, u5iis the signed sum of

speed of rotation of all propellers. The rotational inertia of the drone iis expressed as (Iix ,Iiy,Iiz).Jis the total inertia of the

motor. The payload as shown in Fig. 2(a) is considered to be rigid cylinder of length d, with uniformly distributed mass mp.

Let r= [X,Y,Z]Tbe the position vector of the center of mass of the payload relative to the ﬁxed inertial frame εx0,y0,z0. The

orientation of the payload is expressed in Euler angles as κ

κ

κ= [α,β,γ]Twhere αis the roll angle about the x-axis which is

described as tilt angle and is the main constituent in the load distribution strategy, βis the pitch angle about the y-axis, and γ

is the yaw angle about the z-axis of the payload which are ﬁxed in this case.

4

(a) Free body diagram of dual-UAV-payload system with payload in tilted

orientation.

(b) Description of payload geometric parameters

Fig. 2. Payload geometric parameters and freebody diagram

2.3 Power consumption by motors

As in our previous work [25], an empirical equation between the rotor speed and the power consumption is obtained

using curve ﬁtting as shown in Eq. 7 , for the platform used in this study. The data-set for the empirical equation was obtained

by performing lab tests using thrust stand and was also compared with [26] for the same propulsion system.

PiN =2×10−8×ω3.3659

iN (7)

Where PiN is the power consumed by rotor Nof the UAV i, and ωiN is the speed of the rotor in rad/s. The speed of the

rotors is found using the relation TiN =kbω2

iN where kb=9.85 ×10−6, where TiN is the thrust produced by the rotor Nof

multirotor iand kbis the co-efﬁcient of lift of the propellers. The predicted power consumption of two UAVs carrying jointly

equal load while hovering was compared against the experiment results as it will be shown in Section 5.

3 Energy aware collaboration strategy for 2D object

Given the state of charge of two UAVs to be used for joint payload transportation, the mission success and failure is

tested via simulation methodology presented in this paper. Based on the state of charge of the batteries, the load can be

distributed between the UAVs, using the strategy described in Algorithm 2. The steps presented in Algorithm 2 are described

in this section in detail. This section will describe the system model, power distribution, load distribution, the collaborative

transport strategy, and the constraints that should be considered while using this energy distribution strategy.

3.1 Load distribution

Assuming a payload of weight wand length d, and considerable height is carried by two UAVs, via cable as shown

in Fig. 2(a). The mass distribution is assumed to be uniform, hence center of mass of the payload is assumed to be the

geometrical center of the payload. The free-body diagram of the UAV payload system is shown in Fig. 2(a). The lift force

exerted on the payload by each UAV can be found by using Newton‘s 2nd law and summation of moments around the

payload CoG. Let fibe the lift force exerted by the UAVs on the payload, while diis the distance from the center of mass

of the payload to the point of application of force fi. Using moment summations, we know that the ratio f2

f1and ratio d1

d2are

equal. Thus the required force distribution can be used to ﬁnd the required moment arm ratios d2

d1. The next step is to ﬁnd

the UAV conﬁguration in air that can provide the desired ratio d2

d1. If the tilt of the payload is α, the sum of d1and d2can be

expressed as

d1+d2=dcosα(8)

α=90 −ϖ−sin−1(d2

hd

)(9)

5

Fig. 3. Sensitivity of load-distribution potential vs tilt (α), for various aspect ratios (AR)

Where hdis the half of the diagonal length, ϖis the angle of the diagonal with the base of the payload as shown in Figure 2(b).

For a given value of tilt angle αEq. 8 and Eq. 9 can be solved to ﬁnd the ratio, d2

d1, so iteratively, value of αcan be found for

which the d1

d2is equal to the desired ratio. αcan be used to ﬁnd the required elevation of the drones using ∆h=dsinα.

3.2 Load distribution capacity

The load distribution formulation was used to plot the variation of load distribution potential as represented by d2

d1versus

the tilt angle αfor payloads with different aspect ratio in Fig. 3. The y-axis shows the values between 0 and 1 where 1

represents equal load sharing, 0.5 means that drone02 is carrying half of the load as drone01, while 0 means that drone02 is

not carrying any load. Similarly d1

d2can be plotted to show an increase in the load share of drone02 while decreasing the load

of drone01. Aspect ratio (AR)of the payload, is the ratio of length dof the payload versus the width wpof the payload. The

load distribution sensitivity was found to vary according to the aspect ratio of the payload. As it is shown in Fig. 3, higher

aspect ratios mean that the load distribution is less sensitive to the variation of α. It is also observed that the sensitivity of

load distribution increases signiﬁcantly for higher aspect ratios near 90◦angle. At lower aspect ratios, load distribution is

more sensitive to the variation of the angle α. This implies that the potential of load distribution is higher in lower aspect

ratios. Apart from that, Fig. 3 also presents the limits of load distribution, for example, a payload with aspect ratio of 2,

requires the αto stay below 63◦to have some load distribution, and after 63◦, the load is entirely carried by one UAV. This

is due to the fact that the line of action of lift force of one UAV now passes through the CoG of the payload.

3.3 Power distribution

Assuming that we know the required energy distribution between the two UAVs E2

E1, where E1is the energy level of

drone01 and E2is the energy level of drone02, we can write P2

P1=E2

E1to convert the total energy consumption ratio into

instantaneous power consumption ratio, where P1is the energy level of drone01 and P2is the energy level of drone02. We

can use Eq. 7 for the calculation of the required thrusts u12 and u11. During hovering condition, the thrust u1ican be written

in the following form fi+wi=u1iwhere wiis the weight of the drone i, and fiis the lift force applied to payload by drone i.

This equation is simply showing that the combined thrust applied by the rotors of each UAV must be enough to support the

UAV‘s weight and the lifting force applied to the payload by the UAV.After obtaining the reference thrusts u11 and u12 via

Eq. 7, we can use fi+wi=u1ito ﬁnd the required lift force ratio f2

f1=u12−w2

u11−w1.

6

Fig. 4. Centralized co-ordinated motion collaboration strategy for multi-UAV payload transportation

Algorithm 2: Reference load attitude generation for load distribution strategy

Result: ∆h,α

Input : E1,E2,mp,w1,w2,hd,ϖ

Output: α

P2

P1=E2

E1;

P2

P1

→u12/u11 ;

u12

u11

→f2/f1;

f2

f1

→-d1/d2;

−d1

d2,hd,ϖ→α;

3.4 Constraints

Given the available energy values, we ﬁrst determine the required thrust u1i, which should satisfy the constraints,

u1i−max >u1i>wi, because if the required thrust is lower than the weight of the UAV itself, or higher than the maxi-

mum possible thrust, the mission cannot proceed further. Another constraint is the minimum distance allowed lmin between

two UAVs for collision prevention, and also to avoid any aerodynamic inﬂuence of one UAV to the other. lmin can be used

to ﬁnd αmax using dcosαmax >lmin . The minimum distance, can also be inﬂuenced by the possibility of any collision of the

payload with the UAV rotors. The length of the gripper cable can inﬂuence the maximum tilt αmax . If lsbe the safety factor

to deal with position errors and external disturbances, lgis the length of the gripper, lris the distance between the autopilot

(Center of gravity of hex-rotor) and the rotor tip then we can use trigonometric relations to ﬁnd αmax.

3.5 Collaboration strategy

A co-ordinated motion strategy with a centralized trajectory controller is used in this paper for testing the power dis-

tribution mechanism as shown in Fig. 4. The centralized trajectory controller is responsible for synchronized motion of the

UAVs. The centralized trajectory controller, continuously monitors the error between desired pose for both UAVs and the

current pose, when the error is lower than the pre-deﬁned tolerance, the next way-points are sent to both UAVs at the same

time. This collaboration strategy requires fast and reliable communication between UAVs and the central computer. The

control of the multi-UAV system relies on the individual low level position controllers of each multi-rotor. It is therefore

signiﬁcant that these individual controllers are properly tuned. The motion controllers for both drones consist of a position

controller (P), which generates velocity set-points, a velocity controller (PID), which generates the attitude set-points, and

the attitude controller (PID) generates the required motor RPM set-points. This collaboration strategy was tested in software

in the loop simulations (SITL) and laboratory experiments as shown in the video [27].

4 Simulation methodology and results

The strategy mentioned in this paper although tested on hex-rotor platform, is applicable to multi-rotors and helicopters

in general. Two DJI F-550 models weighing 3.2 Kg each and payloads were simulated using Simulink. Simulink has been

used by [28,29] for modeling of a UAV. The system model as described in Sections 2.2 and 3.1 is implemented using Simulink

for numerical solution of differential equations and modeling of the payload. A complete detail of the model is described in

Fig. 5. The power consumption calculation used in this model is described in Section 2.3. The payload is modeled as a rigid

7

Fig. 5. A complete description of numerical simulation model components used for the veriﬁcation of load distribution strategy.

body with dimensions as described in Section 3.1, which is subjected to lift force and translational force provided by the

UAVs. The translational force is assumed to be equally distributed between the UAVs, however the lifting force is calculated

using the altitude difference of the two drones using the formulation described in Section 3.1. The collaborative transport

strategy and the motion controllers, used in this Simulink model are described in the Section 3.5. The altitude, attitude and

position controllers were added to the Simulink model and tuned. All controller gains, rotor parameters, UAV inertia, UAV

mass, used in the simulation were taken from [25]. Simulation tests were performed in two stages, ﬁrst stage is the base

case simulations, where the results were compared with the hardware experiments. The second stage is where the simulation

results were extended to test extreme cases of load distribution.

4.1 Base case simulations

In base case simulation, the payload considered was a 586 g rectangular beam with dimensions[1.6×0.5×0.1]m. Two

DJI F-550 models named as drone01 and drone02 were considered with energy levels of 37 kJ and 34.5 kJ respectively. At

ﬁrst the simulation was performed with equal energy distribution. It was found via simulations that in order to transport the

payload, while sharing the load equally, each drone will need 36.9 kJ of energy. The drone02 with 34.5 kJ battery failed

while transporting the payload back and forth from −0.2mto1.4 m in y-axis as shown in Fig. 6(c) in red, and hence the

mission was not successful.

The load distribution strategy as described in Section 3.3 was applied and a 6.2 % power consumption ratio was consid-

ered. Based on this ratio, payload roll angle α=37◦was proposed to achieve a lift force distribution of 62 % and 38 %. A

minimum horizontal distance of 1.32 m, with an elevation difference of 1 m between the drones was required to achieve this

load distribution. All other constraints discussed were satisﬁed. When the lift force distribution was applied, the resulting

power consumption by the two drones was 36.75 kJ and 34.25 kJ respectively, proving the effectiveness of the proposed

strategy. The results obtained via the simulation tests are shown in ﬁrst column in Fig. 6 which can be compared to the

experimental results in the second column as shown in Fig. 6. The details of experimental setup and methodology is ex-

plained in Section 5. The red color represents the transportation with equal load sharing, while black color represents the

collaborative transport with strategic load sharing. The dashed line represents drone02 while solid line represents drone01.

4.2 Extended simulated results

Extended simulation experiments were performed with higher load distributions and energy consumption ratios. Several

collaborative transport experiments were performed with equal load sharing and unequal load sharing as shown in the Ta-

ble. 2. The simulations were performed for payloads of range 0.75−1.5 Kg mass and [1.66 ×(0.75 −1)×0.1]m dimensions.

Two DJI-F550 platforms with energy differences of 19.86,24.84,26,33.12% are considered. Two cases each were simulated

with and without load sharing strategy for each energy state. The Table. 2 shows a maximum of 74−26% lift force sharing

and a maximum of 33.12% of energy sharing. It can be seen in Table. 2 that several conﬁgurations of energy levels result in

mission failure with equal load sharing. Therefore the load sharing is performed based on the proposed strategy which leads

to accomplish the mission successfully.

5 Experimental results and discussions

The system hardware consists of one ground station, and two DJI-F550, with Pixhawk autopilot with PX4 ﬁrmware

activation and deactivation only; therefore it was powered by the same battery that powered the drone. The EPM was

activated and deactivated using a ROS node. A force sensor is placed between the triangular 3D printed frame and magnetic

8

(a) Drone altitudes in simulation (b) Drone altitudes in experiment

(c) Trajectory of the drones while transporting the payload in

simulations

(d) Trajectory of the drones while transporting the payload dur-

ing experiments

(e) Relative positions of the drone during simulations (f) Relative positions of the drone during experiments

(g) Lift force distributions in simulation (h) Lift force distributions in experiment

(i) Power consumptions in simulation (j) Power consumptions in experiment

Fig. 6. First and second column represent similar experimental and simulation scenarios

9

Table 2. Extended simulations with various payload shapes and energy states

Payload mass shape ∆Eαf1/f2outcome

1Kg [1.66m×1m×0.1m]0% 0◦50% −50% Failure

1Kg [1.66m×1m×0.1m]24.84% 46◦81% −19% Success

1.5Kg [1.66m×1m×0.1m]0% 0◦50% −50% Failure

1.5Kg [1.66m×1m×0.1m]33.12% 46.29◦81% −19% Success

1.5Kg [1.66m×0.75m×0.1m]0% 0◦50% −50% Failure

1.5Kg [1.66m×0.75m×0.1m]26% 46.29◦74% −26% Success

0.75Kg [1.66m×1m×0.1m]0% 0◦50% −50% Failure

0.75Kg [1.66m×1m×0.1m]19.86% 46.29◦81% −19% Success

gripper as shown in Fig. 7(b). The force sensor (FSE1001) is uniaxial force sensor which transmits the force values using

the USB port of the computer mounted on the drone. The data received by the force sensor is converted into force values

using a ROS node and is published on a ROS topic with a frequency of 150 Hz. A ground station with ROS Master works

as centralized station to communicate and command both drones via wireless connection. Three sets of experiments were

conducted to validate the load sharing method for collaborative transport. First, baseline tests were performed to benchmark

the power consumption of both drones as explained in subsection 5.1. After that, the payload was lifted and kept in hover

by the drones while sharing the load in the second set of experiments which are explained in subsection 5.2. In the last

experiment, collaborative transport was performed with equal and uneven load sharing as described in subsection 5.3.

5.1 Baseline test

Firstly a baseline hovering power consumption test was performed. In this test drone01 and drone02 took off together

autonomously and reached the same altitude. The drones were hovering without any external payload while power con-

sumption was recorded which illustrated that the power consumption proﬁle is similar for both drones as shown in Fig. 8. A

similar test was conducted where both drones were jointly carrying the payload while sharing the payload equally. It can be

observed in the Fig. 8 that both drones are now consuming an increased amount of power due to payload addition, and the

amount of power consumed by both drones is similar.

5.2 Load sharing in hover

The aim of load sharing experiment is to observe the effect of spatial conﬁguration of the drones on the power consump-

tion. A payload equivalent of [1.6×0.5]m of mass 580 g is constructed using two lightweight aluminum rods of length

0.25 m rigidly ﬁxed perpendicular to a 1.6 m rod of rectangular cross-section as shown in Fig. 7(d). The aspect ratio of the

equivalent selected payload is 3.32. The mass of the 1.6 m rod being signiﬁcantly greater than the 0.25 m aluminum rods

makes it possible to have the center of mass of the payload at the center of the 1.6m rod, mimicking a beam of [1.6×0.5]m

of mass 580 g. The payload is already attached to the gripper of the drones. The experiment consists of autonomous takeoff

of the drones with payload where both drones are at the same altitude, and then achieving desired spatial conﬁguration for

both drones. The altitude difference of the two drones was selected with an increment of 0.25 m from 0 to 1.25 m. The

experiments were constrained to avoid ground effects while staying within the range of Optitrack system and the payload

weight chosen based on the payload limitations of the drones. Further increase in altitude difference from 1.25 m resulted

in violation of geometric constraint as shown in the experiment video2. The drones start by taking-off together with the

payload, then achieving same altitude, and wait for 5 seconds to stabilize in the same altitude. After that the desired altitude

difference is achieved and maintained for 150 seconds. The instantaneous power consumption for all cases for both drones is

shown in Fig. 9(b), which shows the incremental difference in power consumption by both drones with incremental change

in the altitude. Total energy consumption is then calculated for each drone. A comparison is made between the percentage

difference of total energy consumption between the two drones for each tilt angle αas shown in Fig. 9(a). The total energy

for each case is found by integrating the instantaneous power over the time of ﬂight. After ﬁnding the total energy for each

2https://youtu.be/o2K4BWfRGHk

10

(a) The drone DJI F550 experimen-

tal platform

(b) EPM gripper with force sensor

(c) The connections between the computer, autopilot, EPM force sensor

and eloggers

(d) Drone01 and drone02 during experiment

Fig. 7. A description of the hardware used in the experiments. The payload, hex-rotors, gripper with force sensor and EPM is also shown

Fig. 8. Instantaneous power and energy consumption by both drones, with and without payload, where dashed lines represent energy

consumption of drones with payload

drone, the percentage energy consumption difference is calculated and plotted in Fig. 9(a). It can be seen in Fig. 9(a) that

the experimental results are in agreement with the simulated results. These experiments provide the proof of concept of the

load distribution which can be achieved by manipulating the orientation of the payload. It is also observed here that power

consumption varies with time, showing an increase in power consumption of drone carrying heavier load. Future work will

include improvement of the strategy to account for such increase. A video demonstration of the whole set of experiments

can be accessed via link2.

11

0 10 20 30 40

0

1

2

3

4

5

6

7

8

Energy diff (%)

Experiment

Simulation

(a) ∆Evs tilt angle αbetween two drones for simulation and

experiments

(b) Power consumption at various tilt angles for corresponding

altitude differences of 0.25-1.25 m, arrows are used to hint the

corresponding pair of drones during one test

Fig. 9. Power consumption during load sharing in hover

5.3 Load sharing in collaborative transport

Two tests were conducted to demonstrate the collaborative transport via load sharing. In these test, drones autonomously

takeoff while jointly carrying the payload to the transportation altitude. In the ﬁrst test, the collaborative transport was

performed via equal load sharing i.e. the transportation altitude set-point was the same for both drones. In the second test,

collaborative transport was performed via uneven load distribution i.e drone01 was given a high altitude set-point compared

to drone02. The second test was aimed to distribute the lifting load 62% and 38% to drone01 and drone02 respectively,

to achieve a 6.2% distribution of energy consumption. This means that if the energy level of drone02 is 6.2% lower than

drone01, the distribution of load will still make the transportation possible. This test is the replication of the simulation

test performed in the previous Section 4.1 with the models using the same hardware. Both tests successfully demonstrated

the to and fro transportation of a 580 g payload in y-axis between −0.2 to 1.2 m in the lab. The test results were obtained

and plotted in Fig. 6. Speciﬁcally, Fig. 6(d) shows the to and fro lateral translational trajectory for the transportation of

the payload. In both cases, the drones are able to transport the payload in a similar manner even when they are unevenly

distributing the lifting force of the payload. The lifting force was distributed via changing the vertical spatial conﬁguration

of the drones relative to each other which is shown in Fig. 6(b). The lift force data obtained by the force sensors is presented

in Fig. 6(h). Fig. 6(f) shows the relative trajectories of the drones in both cases. The instantaneous power consumption for

both drones is shown in Fig. 6(j), which shows similar values as compared to the simulation results shown in Fig. 6(i) and

the resulting energy consumption difference is found to be 6% which is very close to the predicted value of 6.2%. The error

between numerical simulations and experiments, can be attributed to the unaccounted aerodynamic perturbations, caused by

the close proximity of drones while in ﬂight. A detailed video of the collaborative transport with load sharing is available

at [27].

6 Conclusion and future work

This research study proposed an easy to implement multi-UAV collaborative aerial transport strategy with load distri-

bution capability. A load sharing strategy was proposed to deal with uneven battery levels that can ensure the success of the

mission. The constraints and limitations of the load sharing strategy were also discussed. A simulation was performed using

a hex-rotor-payload model developed using Simulink. The effectiveness of the proposed strategy was demonstrated using

an example case. Several experiments were conducted to demonstrate the effect of spatial conﬁguration of the drones on the

force distribution and the power consumption. Speciﬁcally the experiments demonstrated a 62% −38% force distribution to

achieve approximately 6.2% power consumption distribution using simulations and 6% power distribution in hardware ex-

periments based on two hex-rotors UAVs. Extended simulations were also performed to achieve a maximum of 81% −19%

lift force distribution to distribute the power 33.12% between the two UAVs. Current work could be expanded to load sharing

amongst more than two UAVs. Future work will include the effect of shielding of the thrust airﬂow of rotors by the payload

and how to mitigate such effect.

12

Acknowledgements

This publication is based upon work supported by the Khalifa University of Science and Technology under Award No.

RC1-2018-KUCARS.

References

[1] Lee, H., and Kim, H. J., 2017. “Estimation, control, and planning for autonomous aerial transportation”. IEEE

Transactions on Industrial Electronics, 64(4), pp. 3369–3379.

[2] Stolaroff, J. K., Samaras, C., ONeill, E. R., Lubers, A., Mitchell, A. S., and Ceperley, D., 2018. “Energy use and life

cycle greenhouse gas emissions of drones for commercial package delivery”. Nature communications, 9(1), p. 409.

[3] Mohiuddin, A., Tarek, T., Zweiri, Y., and Gan, D., 2020. “A survey of single and multi-uav aerial manipulation”.

Unmanned Systems.

[4] Kim, S., Seo, H., Choi, S., and Kim, H. J., 2016. “Vision-guided aerial manipulation using a multirotor with a robotic

arm”. IEEE/ASME Transactions on Mechatronics, 21(4), pp. 1912–1923.

[5] Mellinger, D., Shomin, M., Michael, N., and Kumar, V., 2013. “Cooperative grasping and transport using multiple

quadrotors”. In Distributed autonomous robotic systems. Springer, pp. 545–558.

[6] Maza, I., Kondak, K., Bernard, M., and Ollero, A., 2010. “Multi-UAV cooperation and control for load transportation

and deployment”. Journal of Intelligent and Robotic Systems: Theory and Applications, 57(1-4), pp. 417–449.

[7] Masone, C., B ¨

ulthoff, H. H., and Stegagno, P., 2016. “Parameters identiﬁcation of thrust generation subsystem for small

unmanned aerial vehicles”. In International Conference on Intelligent Robots and Systems, IEEE, pp. 1623–1630.

[8] Gassner, M., Cieslewski, T., and Scaramuzza, D., 2017. “Dynamic Collaboration without Communication: Vision-

Based Cable-Suspended Load Transport with Two Quadrotors”. In IEEE International Conference on Robotics and

Automation (ICRA), IEEE, pp. 5196–5202.

[9] Tagliabue, A., Kamel, M., Verling, S., Siegwart, R., and Nieto, J., 2017. “Collaborative transportation using MAVs via

passive force control”. In International Conference on Robotics and Automation (ICRA), IEEE, pp. 5766–5773.

[10] Lee, H., Kim, H., and Kim, H. J., 2016. “Planning and control for collision-free cooperative aerial transportation”.

IEEE Transactions on Automation Science and Engineering.

[11] Loianno, G., and Kumar, V., 2018. “Cooperative transportation using small quadrotors using monocular vision and

inertial sensing”. IEEE Robotics and Automation Letters, 3(2), pp. 680–687.

[12] Gioioso, G., Franchi, A., Salvietti, G., Scheggi, S., and Prattichizzo, D., 2014. “The ﬂying hand: A formation of UAVs

for cooperative aerial tele-manipulation”. In International Conference on Robotics and Automation, IEEE, pp. 4335–

4341.

[13] Mohammadi, M., Franchi, A., Barcelli, D., and Prattichizzo, D., 2016. “Cooperative aerial tele-manipulation with

haptic feedback”. In International Conference on Intelligent Robots and Systems, IEEE, pp. 5092–5098.

[14] Michael, N., Fink, J., and Kumar, V., 2011. “Cooperative manipulation and transportation with aerial robots”. Au-

tonomous Robots, 30(1), pp. 73–86.

[15] Jiang, Q., and Kumar, V., 2013. “The inverse kinematics of cooperative transport with multiple aerial robots”. IEEE

Transactions on Robotics, 29(1), pp. 136–145.

[16] Fink, J., Michael, N., Kim, S., and Kumar, V., 2011. “Planning and control for cooperative manipulation and trans-

portation with aerial robots”. The International Journal of Robotics Research, 30(3), pp. 324–334.

[17] Erskine, J., Chriette, A., and Caro, S., 2019. “Wrench analysis of cable-suspended parallel robots actuated by quadrotor

unmanned aerial vehicles”. Journal of Mechanisms and Robotics, 11(2), p. 020909.

[18] Jiang, Q., and Kumar, V., 2012. “Determination and stability analysis of equilibrium conﬁgurations of objects sus-

pended from multiple aerial robots”. Journal of Mechanisms and Robotics, 4(2), p. 021005.

[19] Tognon, M., Gabellieri, C., Pallottino, L., and Franchi, A., 2018. “Aerial co-manipulation with cables: The role of

internal force for equilibria, stability, and passivity”. IEEE Robotics and Automation Letters, 3(3), pp. 2577–2583.

[20] Estevez, J., and Gra˜

na, M., 2017. “Improved Control of DLO Transportation by a Team of Quadrotors”. In International

Work-Conference on the Interplay Between Natural and Artiﬁcial Computation, Springer, pp. 117–126.

[21] Pizetta, I. H. B., Brand˜

ao, A. S., and Sarcinelli-Filho, M., 2016. “Cooperative quadrotors carrying a suspended load”.

In International Conference on Unmanned Aircraft Systems (ICUAS), 2016, IEEE, pp. 1049–1055.

[22] Gimenez, J., Gandolfo, D. C., Salinas, L. R., Rosales, C., and Carelli, R., 2018. “Multi-objective control for cooperative

payload transport with rotorcraft UAVs”. ISA transactions, 80, pp. 491–502.

[23] Dai, X., Quan, Q., Ren, J., and Cai, K.-Y., 2018. “Efﬁciency optimization and component selection for propulsion

systems of electric multicopters”. IEEE Transactions on Industrial Electronics.

[24] Morbidi, F., Cano, R., and Lara, D., 2016. “Minimum-energy path generation for a quadrotor UAV”. In IEEE Interna-

tional Conference on Robotics and Automation (ICRA), IEEE, pp. 1492–1498.

[25] Mohiuddin, A., Tarek, T., Zweiri, Y., and Dongming, G., 2019. “UAV payload transportation via RTDP based optimized

velocity proﬁles”. Energies, 12(16).

13

[26] Filatov, D. M., Friedrich, A. I., and Devyatkin, A. V., 2017. “Parameters identiﬁcation of thrust generation subsystem

for small unmanned aerial vehicles”. In II International Conference on Control in Technical Systems (CTS), IEEE,

pp. 381–383.

[27] Mohiuddin, A. Youtube video title: Energy Estimation and distribution in Dual-UAV collaborative transportation

through load sharing.

[28] Bin Junaid, A., Diaz De Cerio Sanchez, A., Betancor Bosch, J., Vitzilaios, N., and Zweiri, Y., 2018. “Design and

implementation of a dual-axis tilting quadcopter”. Robotics, 7(4), p. 65.

[29] Pengjie, D., and Yang, S., 2012. “Nonlinear modeling of microminiature multi-rotor aircraft”. Ordnance Industry

Automation, 6, p. 006.

14

List of Figures

1 Payload with respect to body and world frame along with anchor points . . . . . . . . . . . . . . . . . . . 3

2 Payload geometric parameters and freebody diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Sensitivity of load-distribution potential vs tilt (α), for various aspect ratios (AR) . . . . . . . . . . . . . . 6

4 Centralized co-ordinated motion collaboration strategy for multi-UAV payload transportation . . . . . . . . 7

5 A complete description of numerical simulation model components used for the veriﬁcation of load distribu-

tionstrategy.................................................... 8

6 First and second column represent similar experimental and simulation scenarios . . . . . . . . . . . . . . 9

7 A description of the hardware used in the experiments. The payload, hex-rotors, gripper with force sensor

andEPMisalsoshown............................................. 11

8 Instantaneous power and energy consumption by both drones, with and without payload, where dashed lines

represent energy consumption of drones with payload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

9 Power consumption during load sharing in hover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

List of Tables

1 Payload attitude angles for lift load distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Extended simulations with various payload shapes and energy states . . . . . . . . . . . . . . . . . . . . . 10

15