Efﬁcient Deployment of Energy-constrained Unmanned Aerial Vehicles

in 3-dimensional Space

Hunsue Lee, Junghyun Oh, Jaedo Jeon and Beomhee Lee

Department of Electrical and Computer Engineering, Seoul National University, Seoul, Republic of Korea

Keywords:

Multi-robot Path Planning, Unmanned Aerial Vehicle, Deployment, Energy Constraint.

Abstract:

In this paper, we present an efﬁcient approach to deployment for unmanned aerial vehicles (UAVs). For a

number of scattered tasks, we aim to minimize the duration of time that all UAVs reach their task locations.

In our previous work, we suggested the collaborative deployment algorithm for mobile robots using a carrier

robot which transports and deploys the mobile robots. However, the method worked only in 2-dimensional

plane where UAV could not be applied. Therefore, this paper extends the previous work on 3-dimensional

space and gives the relevant algorithm. Finally, we presents the feasibility of the proposed algorithm by

simulation results.

1 INTRODUCTION

As unmanned aerial vehicle (UAV) is widely used,

a number of recent study is putting effort into the

development of UAV systems in robotics. The ad-

vantages of using UAV platform are that the UAV is

suitable for large scale operation such as exploration

(Sujit and Beard, 2008)(Luotsinen et al., 2004)(Su-

jit et al., 2009), simultaneous localization and map-

ping (SLAM) (Caballero et al., 2009), map-building

(Yang et al., 2005), search and rescue (Doherty and

Rudol, 2007)(Ryan and Hedrick, 2005), and surveil-

lance (Semsch et al., 2009).

On the other hand, the use of multi-robot system

(MRS) is unavoidable because the system can pro-

vide ﬂexibility, fault-tolerance, robustness, and cost-

effectiveness (Yan et al., 2013). To use multiple

UAVs, the problem of multi-robot task allocation has

to be addressed. However, the general task allocation

problem is known to be nondeterministic polynomial

(NP) hard, meaning that optimal solutions cannot be

found quickly for large problems (Parker, 2008). The

deployment problem is also related with the task al-

location problem. Therefore, we need to reduce the

amount of computation so that the efﬁcient path can

be generated within a ﬁnite time.

In this study, we use a team composed of two

kinds of heterogeneous robots, one carrier robot (CR)

and several UAVs, as shown in Figure 1. We as-

sume the CR has enough energy to complete a mis-

sion that is transporting and deploying the UAVs.

Figure 1: One Pioneer robot as the CR and two X12s as the

UAVs. The CR and the UAVs can be recognized and located

by using the artiﬁcial landmarks.

By using these two kinds of robots, the battery ex-

penditure of the UAV can be reduced and the total

travel distance of the UAV can be increased. There

are a few studies that use this cooperative strategy

(Wang et al., 2015)(Pei and Mutka, 2012)(Rybski

et al., 2000)(Saska et al., 2012). However, most of the

studies focuses on the mechanical implementation of

the system. Only a few existing studies discuss the

path planning problem (Mei et al., 2006). Finding the

optimal deployment path requires a lot of computa-

tion than the amount of computation for the traveling

salesman problem (TSP) (Lee et al., 2015b). To re-

duce the computation, we divided the tasks into sev-

eral clusters based on the geographical information of

the tasks. Then each optimal deployment location for

each cluster can be found. Finally, the deployment

locations are adjusted and merged into the solution.

446

Lee, H., Oh, J., Jeon, J. and Lee, B.

Efﬁcient Deployment of Energy-constrained Unmanned Aerial Vehicles in 3-dimensional Space.

DOI: 10.5220/0005986904460451

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 2, pages 446-451

ISBN: 978-989-758-198-4

Although the solution does not guarantees the opti-

mality, the efﬁcient path can be generated quickly.

The remainder of this paper is organized as fol-

lows. In Section 2, we give brief description of the

problem which has been presented in our previous

work. In the following section, we address the de-

ployment problem in 3-dimensional space. Then Sec-

tion 4 describes simulation results. Finally, in Section

5, conclusions are drawn, and areas for further work

are discussed.

2 PREVIOUS WORK

2.1 Problem Description

In the given environment, there are m tasks, n UAVs

where n ≥ m, and one CR. The CR’s velocity is v

constant acceleration and deceleration is a

, the max-

imum velocity is v

max

, and the rotating speed is w

The UAVs’ velocity is v

and its maximum traveling

distance is d

max

. Unloading of UAVs takes τ seconds.

Meanwhile, a task and its location is denoted by q and

respectively.

In the previous work (Lee et al., 2015b) (Lee et al.,

2015a), we have formulated the deployment problem

for scattered tasks whose objective is to ﬁnding the set

of optimal deployment points W

. Let T

is the dura-

tion of time that the CR moves to α-th deployment

location w

from the initial location, the CR deploys

i-th UAV, and the UAV moves to the target location

. Then T

is formulated as follows:

∑

k=1



f (w

k−1

) + τ



− v

(1)

By using (1), the objective function can be repre-

sented as follows:

= argminmax

,. ..,T

]

(2)

2.2 Path Planning Method

We also proposed a path planning algorithm of the

CR. If there are two tasks q

and q

as shown in Fig-

ure 2, we can always ﬁnd the optimal deployment lo-

cation w

by ﬁnding the circle of Apollonius O

that

has given ratio of distances |v

max

|/|v

| to two given

points q

and q

Figure 2: Finding the optimal deployment location w

for

two given tasks, q

and q

Figure 3: Example of UAV deployment for two tasks in

50m × 50m × 30m space. We set v

max

= 10.0m/s,w

2.0rad/s, a

= 5.0m/s

,τ = 1.0s,v

= 2.0m/s.

3 UAV DEPLOYMENT IN 3D

SPACE

3.1 Optimal Deployment for Two Tasks

First we extends the simulation space into 3D. Fig-

ure 3 shows the example of UAV deployment for two

tasks in 3D space (W: 50m × D : 50m × H : 30m).

In the ﬁgure, blue diamonds represent the task loca-

tion, white circles represent the UAVs, yellow circles

represent the deployment locations, and the red rect-

angle represent the CR. As the CR cannot ﬂy over

the ground, the coordinate of the CR is remained

in 2D plane. Unless the location of second task is

too far, the optimality of the deployment is achieved

by letting two UAVs reach their location simultane-

ously. However, the result in Figure 3 does not satisfy

the criterion as the previous algorithm works in 2D

plane. Therefore, the deployment location should be

adjusted.

Figure 4 describes how the optimal deployment

location can be obtained. Let z

and z

be the heights

of the tasks q

and q

respectively. If z

= 0 and

= 0, then the optimal deployment location w

1new

for q

and q

in Figure 4 is calculated by ﬁnding ∆d

Efﬁcient Deployment of Energy-constrained Unmanned Aerial Vehicles in 3-dimensional Space

447

Figure 4: Finding the optimal deployment location w

1new

for two given tasks, q

and q

in 3D space.

as follows:

ξ − ∆d

= mv(w

1new

) + τ (3)

where ξ = kw

k, mv(w

1new

) is the duration of

CR’s moving time from w

1new

to w

, and:

S =

+ (ξ − ∆d)

− 2l(ξ − ∆d)cosθ

(4)

rt(θ

1new

) =



∆d

· θ



(5)

where rt(θ

1new

) is the function that returns the dura-

tion of rotating time at the deployment location w

1new

Expanding on this idea, we can ﬁnd ∆d for q

and

by equalizing the durations that ﬁrst UAV moves

from w

1new

to q

, and the CR moves from w

1new

to w

plus second UAV moves from w

to q

as follows:

(ξ − ∆d)

+ |z

= mv(w

1new

)+τ +

(6)

where 0 ≤ ∆d ≤ ξ.

3.2 Clustering of Tasks

To ﬁnd efﬁcient deployment points, we iteratively di-

vide the set of all the tasks into several subsets, which

is refered here as cluster. In 2D space, we ﬁnd mini-

mum bounded circle for each cluster so that the center

and radius of the circle can be found. Therefore, here

we ﬁnd minimum bounded sphere for each cluster of

tasks as follows:

minimize r

subject to kq

− ek ≤ r

(7)

To solve (7), we ﬁrst ﬁnd convex hull (Graham, 1972)

so that only outer points are considered for ﬁnding the

sphere. For α-th cluster of tasks p

, the center of the

bounded sphere (x

) and its radius r

is computed

by ﬁnding three points (x

), (x

) which

satisfy as follows:

Figure 5: Calculation of deployment locations. The loca-

tions are calculated by using the maximum traveling dis-

tance of the UAV, the size of the cluster, and the direction to

the next cluster.

− x

)

+ (y

− y

)

= r

(8)

− x

)

+ (y

− y

)

= r

(9)

− x

)

+ (y

− y

)

= r

(10)

If any r

for a cluster is bigger than d

max

, then the

cluster should be divided until all radii of clusters are

less than or equal to d

max

so that the UAVs deployed

at a deployment location can reach all task locations

in the relevant cluster.

3.3 Determining Deployment Locations

Once a set of clusters is arranged, a series of deploy-

ment locations should be calculated. In the previous

sub-chapter, we addressed the optimal deployment for

two tasks. However, as the number of clusters in-

creases, the UAVs which are deployed in the former

deployment location have enough time to ﬂy. There-

fore, to reduce the overall time, the CR should deploy

UAVs at their maximum traveling distance d

max

un-

less the next cluster is the last.

Figure 5 describes this concept. Let there be two

clusters of tasks, p

and p

α+1

as depicted in Figure

5. Then the CR should stop near by p

ﬁrst, then go

to p

α+1

. Let the center of p

, p

α+1

, and the loca-

tion of the CR be (x

), (x

α+1

), and

,0) respectively. First, we ﬁnd a line segment

between the CR and (x

α+1

,0) which is the pro-

jected point of (x

α+1

) as follows:

y =

α+1

− y

α+1

− x

(x − x

) + y

(11)

where min(x

α+1

) ≤ x ≤ max(x

α+1

). Next, we

ﬁnd an another line segment which is perpendicular

to (10) and crosses (x

,0) as follows:

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

448

y =

− x

α+1

− y

(x − x

) + y

(12)

Then, the deployment location w

can be found as

a dot on (12). To minimize the travel distance of the

CR, we ﬁnd ∆e which satisﬁes the following equation:

(∆e)

+ h

= (d

max

− r

)

(13)

so that the distance from w

to the farthest point

in p

is the same as the maximum traveling dis-

tance of the UAV, d

max

. If a diameter of a cluster is

longer than d

max

, ∆e in (13) cannot be solved because

> (d

max

− r

). Therefore, the deployment point

also cannot be acquired.

4 SIMULATION

4.1 Simulation Environment

The goal of this work is to validate the proposed al-

gorithm in 3D space. We implemented the method

in Matlab for the simulation. The simulated environ-

ment is listed in Table 1. The simulation program is

executed on a computer with dual-core 2.90GHz Intel

Core i5-5287U CPU, 8GB RAM, and Windows 8.1

64bit operating system. Note that the program code is

not fully optimized.

Table 1: The speciﬁcation of the simulation computer

Processor Intel Core i5-5287U 2.90GHz

Memory 8GB DDR3

OS Windows 8.1 (64bit)

4.2 Result

First, the deployment for two tasks is examined. The

result is shown in Figure 6. First, the CR is located in

its initial location in Figure 6(a). In Figure 6(b), the

CR approaches to ﬁrst deployment location w

. As

the CR arrives at w

, the ﬁrst UAV is deployed and it

begins to ﬂy in Figure 6(c). After ﬁnishing all deploy-

ment, two UAVs approach their assigned locations in

Figure 6(d). Finally, two UAVs arrive the locations

simultaneously. From this simulation, we verify the

optimality of the proposed deployement method for

arbitrary two tasks.

The example of more complex scenario for

deployment is given in Figure 7. The spheres

imply the maximum traveling distance of the

UAV from each deployment location. Task loca-

tions are (57,11,4),(76, 59,5), (17,37,6),(13,75,7),

(9,26, 5),(50,70,3). v

max

= 15.0m/s,w

= 3.0rad/s,

= 10.0m/s

,τ = 4.0s,v

= 1.0m/s, and d

max

varies from 7.0m to 35.0m. Figure 7(a) shows the

deployment result when d

max

= 7.0m. According to

max

, six tasks are separated into six clusters. The

CR travels 201.24m, and it takes 52.95s for all the

UAVs reach task locations. Next, the maximum trav-

eling distance increases to 15.0m in Figure 7(b). As

a result, two tasks with respect to w

and w

in Fig-

ure 7(a) are merged into one cluster. In addition, both

the travel distance of the CR and the total duration

of time for deployment decreases. Figure 7(c) shows

the result when d

max

= 25.0m. In the same manner,

both the distance of the CR and the total duration also

decreases, and another two tasks are merged into one

cluster. By using the proposed method, the efﬁcient

path generation for deployment is shown.

5 CONCLUSIONS

In this paper we proposed the UAV deployment algo-

rithm which is efﬁcient and overcomes energy con-

straint of UAVs. By considering geographical ad-

jacency of multiple tasks, the tasks are divided into

several clusters, and then the deployment location for

each cluster is determined by the proposed algorithm.

The deployment location is calculated by consider-

ing the dynamics of CR and UAVs and energy con-

straint of UAV to minimize the duration of time that

all UAVs are reached their given locations. Since the

previously proposed algorithm was applicable only in

2D space, we extended it to 3D space and dealt with

the problems that arose from the dimension. We have

implemented the proposed method in simulation and

showed that the method is feasible and efﬁcient. This

kind of cooperative deployment strategy can be used

for the operations such as drone delivery and plane-

tary exploration.

For future work, we consider belows:

1) Adopting a conventional obstacle avoidance algo-

rithm;

2) Expanding the method to UAV collection prob-

lem;

3) Conducting experiments in real robot platforms;

ACKNOWLEDGEMENTS

This work was supported in part by the Na-

tional Research Foundation of Korea(NRF)

grant funded by the Korea government(MSIP)

(No.2013R1A2A1A05005547), in part by the Brain

Efﬁcient Deployment of Energy-constrained Unmanned Aerial Vehicles in 3-dimensional Space

449

Korea 21 Plus Project, in part by ASRI, and in

part by Samsung Electro-Mechanics Co., Ltd.

REFERENCES

Caballero, F., Merino, L., Ferruz, J., and Ollero, A. (2009).

Vision-based odometry and slam for medium and high

altitude ﬂying uavs. Journal of Intelligent and Robotic

Systems, 54(1-3):137–161.

Doherty, P. and Rudol, P. (2007). A uav search and rescue

scenario with human body detection and geolocaliza-

tion. In AI 2007: Advances in Artiﬁcial Intelligence,

pages 1–13. Springer.

Graham, R. L. (1972). An efﬁcient algorith for determin-

ing the convex hull of a ﬁnite planar set. Information

processing letters, 1(4):132–133.

Lee, H., Jeon, J., and Lee, B. (2015a). An efﬁcient co-

operative deployment of robots for multiple tasks. In

Robotics and Automation (ICRA), 2015 IEEE Interna-

tional Conference on, pages 5419–5425. IEEE.

Lee, H., Yoo, H., and Lee, B. (2015b). Deployment

method of uavs with energy constraint for multiple

tasks. Electronics Letters, 51(21):1650–1652.

Luotsinen, L. J., Gonzalez, A. J., and Boeloeni, L. (2004).

Collaborative uav exploration of hostile environments.

Technical report, DTIC Document.

Mei, Y., Lu, Y.-H., Hu, Y. C., and Lee, C. G. (2006).

Deployment of mobile robots with energy and tim-

ing constraints. Robotics, IEEE Transactions on,

22(3):507–522.

Parker, L. E. (2008). Distributed intelligence: Overview

of the ﬁeld and its application in multi-robot systems.

Journal of Physical Agents, 2(1):5–14.

Pei, Y. and Mutka, M. W. (2012). Steiner traveler: Re-

lay deployment for remote sensing in heterogeneous

multi-robot exploration. In Robotics and Automa-

tion (ICRA), IEEE International Conference on, pages

1551–1556.

Ryan, A. and Hedrick, J. K. (2005). A mode-switching path

planner for uav-assisted search and rescue. In Deci-

sion and Control, 2005 and 2005 European Control

Conference. CDC-ECC’05. 44th IEEE Conference on,

pages 1471–1476. IEEE.

Rybski, P. E., Papanikolopoulos, N. P., Stoeter, S., Krantz,

D. G., Yesin, K. B., Gini, M., Voyles, R., Hougen,

D. F., Nelson, B., Erickson, M. D., et al. (2000).

Enlisting rangers and scouts for reconnaissance and

surveillance. Robotics & Automation Magazine,

IEEE, 7(4):14–24.

Saska, M., Krajn

ık, T., and Pfeucil, L. (2012). Cooper-

ative µuav-ugv autonomous indoor surveillance. In

Systems, Signals and Devices (SSD), 9th International

Multi-Conference on, pages 1–6.

Semsch, E., Jakob, M., Pavl

cek, D., and P

echou

cek,

M. (2009). Autonomous uav surveillance in com-

plex urban environments. In Web Intelligence and

Intelligent Agent Technologies, 2009. WI-IAT’09.

IEEE/WIC/ACM International Joint Conferences on,

volume 2, pages 82–85. IET.

Sujit, P. and Beard, R. (2008). Multiple uav exploration

of an unknown region. Annals of Mathematics and

Artiﬁcial Intelligence, 52(2-4):335–366.

Sujit, P., Sousa, J., and Pereira, F. L. (2009). Uav and auvs

coordination for ocean exploration. In Oceans 2009-

Europe, pages 1–7. IEEE.

Wang, J., Smith, C., Staskevich, G., and Abbe, B. (2015). A

distributed deployment algorithm for mobile robotic

agents with limited sensing/communication ranges. In

Electro/Information Technology (EIT), IEEE Interna-

tional Conference on, pages 530–535.

Yan, Z., Jouandeau, N., and Cherif, A. A. (2013). A sur-

vey and analysis of multi-robot coordination. Interna-

tional Journal of Advanced Robotic Systems, 10.

Yang, Y., Minai, A., and Polycarpou, M. M. (2005). Evi-

dential map-building approaches for multi-uav coop-

erative search. In Proceedings of the American Con-

trol Conference, volume 1, page 116.

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

450

Figure 6: Deployment procedure. (a) Initial state (b) The

CR approaches to w

, and

ﬁrst UAV moves to ﬁrst task location (d) Two UAVs are

approaching (e) All UAVs reach their assigned locations.

Figure 7: Deployment Example for six tasks in (100m ×

100m×30m). We set v

max

= 15.0m/s,w

= 3.0rad/s,a

10.0m/s

,τ = 4.0s, and v

= 1.0m/s. (a) d

max

= 7.0m (b)

max

= 15.0m (c) d

max

= 25.0m (d) d

max

= 35.0m.

Efﬁcient Deployment of Energy-constrained Unmanned Aerial Vehicles in 3-dimensional Space

451