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NAVIGATION SYSTEM FOR
LANDING A SWARM OF
AUTONOMOUS DRONES ON A
MOVABLE SURFACE
Anam Tahir1, a, Jari B¨oling2, b, Mohammad-Hashem Haghbayan1, c, and Juha Plosila1, d
1Autonomous Systems Laboratory, Department of Future Technologies
2Laboratory of Process and Systems Engineering
1University of Turku, 2˚
Abo Akademi University
1,2Turku, Finland
Email: aanam.tahir@utu.fi, bjari.boling@abo.fi, cmohhag@utu.fi, djuha.plosila@utu.fi
KEYWORDS
Unmanned Aerial Vehicles; Distributed Control;
Leader–Follower Hierarchy; Soft Landing
ABSTRACT
The development of a navigation system for the land-
ing of a swarm of drones on a movable surface is one
of the major challenges in building a fully autonomous
platform. Hence, the purpose of this study is to in-
vestigate the behaviour of a swarm of ten drones un-
der the mission of soft landing on a movable surface
that has a linear speed with the effect of oscillations.
This swarm, arranged in a leader–follower hierarchical
manner, has distributed control units based on Linear
Quadratic Regulator control with integral action tech-
nique. Furthermore, to prevent drones from landing ar-
bitrarily, the leader drone takes the feedback of transla-
tional coordinates from the movable surface and adjusts
its position accordingly. Hence, each follower tracks
the leader’s trail with offsets, taking collision avoidance
into account. The design parameters of controllers are
mapped in a way that the simulations demonstrate the
feasibility and great potential of the proposed method.
INTRODUCTION
Unmanned Aerial Vehicles (UAVs), or drones, are
increasingly getting attention in the aviation and mar-
itime industries with the evolution of drone technol-
ogy for both recreational and military grounds [1, 2].
These have innovative impacts in the areas of data col-
lection for inspection purposes and are capable of car-
rying out tasks in a variety of situational operations.
They can shape the future with potential benefits in the
fields such as security and surveillance, remote sensing,
search and rescue, elimination of human error, and au-
tonomous deliveries and shipping [3–6]. For example, in
2017, the European Maritime Safety Agency (EMSA)
issued a contract to Martek, valued at €67M for the
usage of drones in European waters to provide assis-
tance with border control activities, pollution monitor-
ing, search and rescue tasks, and detection of illegal
trafficking (drugs and people) and fishing [7, 8].
The landing mechanism of UAVs is one of the chal-
lenging problems. An extensive survey based on vision-
based autonomous landing methods is elaborated in [9].
Based on the setup of the vision sensors, these methods
are divided into two main categories, i.e., onboard vi-
sion landing systems and on-ground vision systems. In
[10], a detailed review on control based landing tech-
niques (such as from basic nonlinear to intelligent, hy-
brid and robust control) along with GPS and vision-
based landing schemes is presented. A wide literature
is available related to vision-based autonomous land-
ing of UAVs [11–17]. For example, in [18], a vision-
based net recovery landing system is proposed for a
fixed-wing UAV that does not require a runway. Like-
wise in [19], the landing of a quadrotor on a mov-
ing platform is addressed. In [20], a real-time vision-
based landing algorithm for an autonomous helicopter
is implemented. An on-board behaviour-based con-
troller is used that is subdivided into hover, velocity,
and sonar sub-behaviours. Hovering control of the
helicopter is implemented using proportional control,
whereas velocity and sonar controllers are implemented
with proportional-integral control design. In [21], a
nonlinear proportional-integral type controller is pro-
posed for vertical take-off and landing of a quadcopter.
It exploits the vertical optical flow to facilitate hover
and land on a movable platform. In [22], to control a
quadcopter’s vertical take-off and landing on a moving
platform, the image-based visual servoing integrated
with the adaptive sliding mode controller is validated.
However, this approach requires the landing site to be
predetermined and therefore, it is not suitable for op-
erations in unknown terrain.
Due to the rising importance and research effort
put into autonomous vehicles and robots, there is
broad research on vision-based methods integrated
with/without control techniques for landing missions.
Hence, this paper focuses on the control design for land-
ing a swarm of drones on a movable surface, and the
vision-based approaches are of no interest in this work.
Communications of the ECMS, Volume 34, Issue 1,
Proceedings, ©ECMS Mike Steglich, Christian Mueller,
Gaby Neumann, Mathias Walther (Editors)
ISBN: 978-3-937436-68-5/978-3-937436-69-2(CD) ISSN 2522-2414
Landing safely, i.e., soft landing, is the key to suc-
cessful exploration of the assigned missions; in electro-
mechanical systems, the mitigation of the connected
effects of collision relies on the conversion of kinetic en-
ergy into heat or potential energy. An effective landing-
system design should minimize the acceleration act-
ing on the payload. In other words, the major chal-
lenges in autonomous landing are; (a) accurate place-
ments as much as possible on the landing platform, and
(b) the trajectory following in the presence of distur-
bances and uncertainties. Portions of this work have
been reported in the previous work [23]. However, for
present paper, there are additional contributions to face
these challenges. This paper addresses the problem
based on system modelling and testing of a swarm in a
leader–follower hierarchical formation, consisting of ten
drones, aiming at executing missions of soft landing on
an oscillating surface that can be a vessel or any sur-
face having oscillations. The distributed control units
of each quadcopter in the swarm are designed using an
Linear Quadratic Regulator (LQR) with integral action
technique that can handle a multivariable system.
This paper comprises of 6 sections. Section 1, in ad-
dition to introducing the topic, also dwells upon the
significance of the study as well as the works already
carried out in this particular domain. Section 2 dis-
cusses the elements of a swarm formation while Sec-
tion 3 elaborates the composition of swarm formation
of UAVs. Section 4 describes the proposed control de-
sign for soft landing, whereas Section 5 builds upon
the evaluation of the landing missions. Lastly, Section
6 presents the concluding remarks.
COMPONENTS OF A FORMATION
One of the most vital challenges in multi-agent sys-
tems is the formation control. It is defined as an or-
ganisation of a group of agents to maintain a formation
with a certain shape [6]. Three main components are
considered to solve any formation control problem, i.e.,
system architecture, its modelling, and strategies of for-
mation control [24].
System Architecture
The system architecture delivers the infrastructure
upon which formation control is implemented such as:
•Heterogeneity vs. homogeneity: Heterogeneous
teams consist of either different apparatus or software,
whereas homogeneous teams comprise of similar mod-
ules of hardware or software.
•Communication structures: The communication
structures in the swarm can be categorised w.r.t. range,
topology, and bandwidth.
•Centralization vs. decentralization: In the central-
ized controlling approach, a single controller possesses
all the information required to get the desired control
objectives, whereas each agent has its own local control
mechanism and is completely autonomous in the deci-
sion process of decentralized control. Hybrid central-
ized/decentralized architectures, in turn, use central
planners to provide high-level control over autonomous
robots.
System Dynamics
The dynamics of each drone in the swarm is based
on the model of a quadcopter, i.e., a drone that has
four propellers and `is a length of the fixed pitch to
mechanically movable blades, as shown in Fig. 1.
Fig. 1: Kinematics of the quadcopter
The gravity gand the thrust Ti,i∈ {1,2,3,4}, of the
propellers are the main forces acting on the quadcopter.
In this model, the inertial reference is the earth shown
as (x, y, z) that is the origin of the reference frame. The
drone is assumed to be a rigid body that has the con-
stant mass symmetrically distributed with respect to
the planes (x, y), (y, z ), and (x, z). The orientation of
a quadcopter reference frame (x, y, z) with respect to
an inertial frame (x, y, z)0can be expressed mathemat-
ically in a state variable form [25], where translational
and angular accelerations are given by
˙vx=−vzwy+vywz−gsin θ
˙vy=−vxwz+vzwx+gcos θsin φ
˙vz=−vywx+vxwy+gcos θcos φ−T
m
(1)
and
˙wx=1
Jx
(−wywz(Jz−Jy) + Mx−kwT
kMT
JmpMzwy)
˙wy=1
Jy
(−wxwz(Jx−Jz) + My−kwT
kMT
JmpMzwx)
˙wz=Mz
Jz
(2)
respectively. The thrust produced by each propeller
Tiis translated into a total thrust T, and the reactive
torque Mi,i∈ {x, y, z}, is affecting the rotations along
the corresponding axis. Ji,i∈ {x, y, z }, is known as
the moment of inertia along the corresponding axis, and
Jmp is the moment of inertia of a motor with a pro-
peller. The velocities corresponding to Equations (1)
and (2) are
˙x=vxcos ψcos θ+vy(−sin ψcos φ+ cos ψsin θ
sin φ) + vz(sin ψsin φ+ cos ψsin θcos φ)
˙y=vxsin ψcos θ+vy(cos ψcos φ+ sin ψsin θ
sin φ) + vz(−cos ψsin φ+ sin ψsin θcos φ)
˙z=vxsin θ−vycos θsin φ−vzcos θcos φ
(3)
and
˙
θ=wycos φ−wzsin φ
˙
φ=wx+wysin φtan θ+wzcos φtan θ
˙
ψ=wy
sin φ
cos θ+wz
cos φ
cos θ
(4)
respectively. The Equations (1)–(4) represent the com-
plete nonlinear model of a quadcopter, composed of 12
states, 4 inputs, and 12 outputs. More precisely,
x=vxvyvzwxwywzθ φ ψ x y z T(5)
is the state or system vector,
u=T MxMyMzT(6)
is the input or control vector,
y=x(7)
is the output (measured) vector. Furthermore, the per-
formance output
yp=x y z T(8)
is defined for future use.
Using standard linearization, that is cutting off a
Taylor series expansion after the first derivative, the
nonlinear dynamic equations can be converted into lin-
ear state-space equations. This yields,
˙x =h−gθ gφ −T
m
Mx
Jx
My
Jy
Mz
Jzwywxwzvxvy−vziT
y=x
(9)
that can further written into the standard state space
form
˙x =Ax+Bu
y=Cx+Du(10)
where A,B,C, and Dare known as the state or system
matrix, input or control matrix, output (measured) ma-
trix, and feedthrough matrix respectively. Correspond-
ingly, x,u, and yare known as the state or system
vector, input or control vector, and output (measured)
vector as in Equations (5)–(7). The system parameters
are taken from [25] and illustrated in Table I. The lin-
ear model in Equation (10) is used to examine the land-
ing stability and controllability of the system as well as
to design an LQR with integral control. The system has
twelve eigenvalues at the origin, and all twelve states
are controllable.
TABLE I: System parameters
Symbol Quantity Value
ggravitational force 9.81 m/s2
`length of the fixed pitch
to mechanically movable
blades
0.2 m
mmass of quadcopter 0.8 kg
Jmp moment of inertia of motor
with propeller
≈0
Jx, Jymoment of inertia w.r.t.
axis x, y
1.8×10−3kgm2
Jxmoment of inertia w.r.t.
axis z
1.5×10−3kgm2
kMT ratio of the reactive mo-
ment and thrust
0.1 m
Formation Control Schemes
A formation control scheme defines how a group of
robots can be controlled to form and to maintain the
desired formation. To control the formation of a drone
swarm, the recent studies generally classify the different
strategies into following main categories.
•Leader–follower [26–28]: The leader seeks for some
group objectives, while the followers track the leader’s
coordinates with prescribed offsets.
•Virtual structure [29–31]: A virtual moving structure
reflects the complete formation as a rigid body such
that the control design for a single agent is derived
by defining the virtual structure. It then translates
the movement of the virtual structure into the desired
movement of each agent. Furthermore, as an actual
leader is not needed, each virtual vacant pose can be
filled by any agent.
•Behaviour-based [32–34]: each agent is assigned to
the process of actuation that is defined as several de-
sired behaviours. In each agent, to form the desired
shape of the swarm, the overall control is derived by
allocating different weights to behaviours.
The formation control schemes can be further cat-
egorised into position-, displacement-, distance-, and
angle-based in terms of the requirement on the sens-
ing capability and the interaction topology [35]. In
position-based control, each agent is able to sense its
own position in the formation that is defined by the
desired positions of the different agents with respect
to a global coordinate system. In contrast to this, in
displacement-based control, each agent is assumed to
sense its own as well as its neighbouring agents’ po-
sition in the formation that is defined by the desired
displacements between pairs of agents with respect to
the global coordinate system. Then again, in distance-
based control, the formation is defined by the desired
inter-agent distances that are actively controlled. Each
agent in the formation is expected to sense relative posi-
tions of their neighbouring agents with respect to their
own local coordinate systems. Likewise, the actively
controlled variable is the bearing between neighbours
in angle-based control, rather than the distance to each
of the neighbours.
COMPOSITION OF SWARM OF UAVS
Consider a hierarchical formation that has four lev-
els using ten quadcopters, as illustrated in Fig. 2. This
formation is based on a tightly coupled leader–follower
flying mechanism in which the leader is directly com-
municating with its followers by providing its position
references that are passed on to the followers [6,36].
Fig. 2: Organization of the considered swarm of drones
In Fig. 2, the swarm is responsible for tracking the
desired trajectories as well as for hovering at desired
positions for given time intervals. The straight arrows
show the direction in which coordinate variables are
shared. The leader’s trajectory is independent and de-
fines the formation’s trajectory. The trajectory of each
follower is defined based on the orientation and actions
of its respective leader. In terms of movement, each
follower is dependent on its respective leader’s move-
ment using a safe distance strategy that is denoted by
dα,β , where α, β ∈ {L,1–9}. Each follower is responsi-
ble for efficiently tracking the respective leader’s trajec-
tory, maintaining the distance between two respective
entities.
To address the research questions, consider a control
system that is liable for fine-tuning the movement of
each drone in a swarm while maintaining the desired
safe travel distance. Each drone is based on the similar
system dynamics, which is illustrated in Section 2. In
Fig. 3, a simple mechanism of feedback control system
is presented in which output is controlled using its mea-
surement as a feedback signal. This feedback signal is
compared with a reference signal to generate an error
signal which is filtered by a controller to produce the
system’s control input.
PROPOSED CONTROL DESIGN FOR SOFT
LANDING
In a simple example illustrated in Fig. 4, the swarm
of drones aims to land on a vessel (or any type of mov-
Fig. 3: Transmission topology in swarm formation
able surface) that has continuous speed with oscilla-
tions. It is assumed that the data is available through
communication link on-board drones and vessel.
Fig. 4: Arrival of the swarm of drones for landing
In Fig. 4, the reference commands of a moving ves-
sel are continuously sent to the leader drone as a feed-
back (red arrow line), outlining a tracking phenomenon.
The local control unit of the leader then computes the
values under its vicinity and generates the force in
order to stabilize its landing movement (green arrow
line). This process continuous until the desired goal
is achieved. Since, the designed formation is based
on a leader–follower tightly coupled approach there-
fore, all the followers track their corresponding lead-
ers, which can minimize the overall computation time
of path planning, indicating the fast decision making
within the swarm. A filter block (see Appendix) is in-
cluded in the altitude of the leader drone to slow down
its speed on a close arrival by avoiding sudden hit on
the surface.
For the controlled movement of each quadcopter in
the swarm, the initial step is to construct a balanced
drone in the presence of uncertainties and external dis-
turbances with an adaptive computing platform. For
this study, a standard LQR with integral action tech-
nique has been adapted [36]. Based on the linear model
in Equation (10), LQR is a way of finding an optimal
full state feedback controller for each quadcopter. Fig.
5 shows the decision-making process of a drone that
is split into two feedback loops, i.e., inner and outer
loops. The inner loop is the full state feedback system
and the outer loop is responsible for the x,y, and z
positions, generating the thrust Tand the torques Mi.
Fig. 5: Block diagram of the control design
The control input uminimizes the quadratic cost
function
J(u) = Z∞
0
(˙xT
aQ˙xa+˙uTR˙u)dt (11)
where Qand Rare known as the weight matrices (see
Appendix), and uis given in Equation (6). The Qma-
trix is a positive semi-definite that defines the weights
for the states, whereas the Rmatrix is a positive def-
inite that indicates the weights of the control inputs.
The controller can be tuned by changing the entries in
the Qand Rmatrices to get the desired response. LQR
method returns the solution Sof the associated Riccati
equation
(A)TS+SA −SBR−1(B)TS+Q= 0 (12)
for S=ST>0. The optimal gain matrix Kis derived
from Sas K=R−1(B)TS. The four control inputs are
generated for thrust T,Mx(along x-axis i.e., roll φ),
My(along y-axis i.e., pitch θ), and Mz(along z-axis
i.e., yaw ψ) using state feedback law,
u=Ki
se−Kpx,(13)
where e=r−yp,r= [xryrzr]T,ypis given in
Equation (8), Kiis the integral gain, and Kpis the
state feedback gain.
RESULTS
The landing of the swarm of drones on a movable
surface (can be defined as a vessel) that has continuous
speed with oscillations, which is moving from south-
west to north-east, is considered with a smallest mar-
gin of error. The simplest model of a movable sur-
face Vis defined as a ramp function with a slope of
0.5t. The oscillations of a movable surface are defined
as sine wave with amplitude of 1m, and frequency of
0.1rad/sec. Since the swarm is arranged in a tightly
coupled leader–follower hierarchical formation, the ref-
erence signal of the leader drone is available to its im-
mediate follower(s). Thus, the followers track the out-
put of the leader with set distance. The initial time
t= 0s while the landing occurs at time t= 15s, are
set in the references of the leader drone. The refer-
ence positions of the leader drone are x=y= 2, and
z= 10 −→ 0 with step time t= 15s. The initial
launching position xof each drone is set to 7m away
from its respective neighbouring node(s), and the fur-
ther data for simulation is shown in Table II. Simula-
tions in Simulink®MATLAB are used for the evalu-
ation of the proposed method. In all simulations, the
sampling time tsof 0.01s is used for all the figures.
TABLE II: Initial positions (m) and offsets (m) of
drones used in simulation
Drones Symbol Initial Position
(x, y, z)∗
Offset
(x, y, z)∗
Leader L (0,0,10) –
Follower 1 f1 (7,0,10) (9,0,0)
Follower 2 f2 (−7,0,10) (−5,0,0)
Follower 3 f3 (14,0,10) (9,0,0)
Follower 4 f4 (21,0,10) (16,0,0)
Follower 5 f5 (28,0,10) (23,0,0)
Follower 6 f6 (−14,0,10) (−5,0,0)
Follower 7 f7 (−21,0,10) (−12,0,0)
Follower 8 f8 (35,0,10) (16,0,0)
Follower 9 f9 (−28,0,10) (−12,0,0)
The landing mechanism on a movable surface is
shown in Fig. 6(a) and (b). The orientation of the
surface is available as a feedback at the leader drone
that resulted in accurate landing with negligible errors.
Hence, each follower track the reference commands that
are defined by its respective leader and the pre-specified
formation. To avoid collisions in the swarm, there is a
gap of 7m in xpositions for all the drones with their
neighbouring peer(s). Therefore, it is evident that the
landing of all the drones is occurred in a straight line
with different xpositions. Furthermore, the total ki-
netic energy, KE, produced by the swarm due to its
motion versus the total stored potential energy, P E
is described in Fig. 6(c). Total energy possessed and
held in the swarm are calculated as KE = 0.5mv2and
P E =mgh respectively. These energies relate how
much work is conserved in the process of the swarm
movement.
The trajectory errors, {ex, ey, ez}, between the ori-
entation of the movable surface Vand the drones are
illustrated in Fig. 7(a), (b), and (c). The trajectory er-
ror ezis sometimes positive in Fig. 7(c) because zposi-
tion is different depending on yposition, and the drones
land at different positions and/or time instances.
CONCLUSION
This paper addressed one of the interesting chal-
lenges in employment of swarming drones, namely land-
ing softly/safely on a movable surface. More specifi-
cally, a setup is considered where a swarm of ten drones
in a hierarchical leader–follower formation aims at land-
(a) 3D view (b) top view (c) Sum of kinetic vs. potential energies,
the drones are moving with the ship after
landing
Fig. 6: Landing placements of swarming drones
(a) (b) (c)
Fig. 7: Trajectory errors between movable surface and corresponding drone
ing on a moving vessel that has a linear speed under
the effect of oscillations. In the proposed distributed
control system design, each drone in the swarm has a
local controller based on an LQR with integral action
technique that is an optimal control method providing
the smallest possible error to its input. To avoid any
collisions among drones in the swarm, a safe travel dis-
tance strategy using offsets is employed in the overall
system. In the considered scenario, each drone is al-
ready at a specific altitude and from there it lands. The
swarm is composed of tightly coupled agents, where
each drone in the swarm is directly communicating,
using shared coordinate variables, with its immediate
associate. Therefore, the leader of the swarm is respon-
sible for the execution of the path planning algorithm.
It takes the translational measurements of the movable
surface as a feedback in order to generate the landing
coordinates. It is evident from the simulation results
that the proposed system guarantees the convergence
of the desired landing missions on the movable surface
while minimizing the possibilities for landing errors.
The other key advantages of the proposed method are
its robustness and scalability. Furthermore, It is un-
derstandable from the graphs that the control strategy
permits the intuitive execution of an extensive variety
of the swarm behaviours.
APPENDIX
Q= diag
0.0885,4.6064e−04,6000,1080,1080,
1080,180,180,180,0.0147,7.6773e−05,
1000,0.4423,0.0023,30000
R=I4
Filter block Gr={Gxr, Gyr, Gzr}. For the leader
drone, Gxr=Gyr= 1, and Gzr= state-space model
in which A=−1/12, B= 1/12, C= 1, D= 0,
and initial conditions = 10. For all the other drones,
Gr={Gxr, Gyr, Gzr}={1,1,1}
ACKNOWLEDGEMENTS
This work has been supported in part by the
Academy of Finland, project no. 314048.
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