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Two important aspects in dealing with autonomous navigation of a swarm of drones are collision avoidance mechanism and formation control strategy; a possible competition between these two modes of operation may have negative implications for success and efficiency of the mission. This issue is exacerbated in the case of distributed formation control in leader-follower based swarms of drones since nodes concurrently decide and act through individual observation of neighbouring nodes’ states and actions. To dynamically handle this duality of control, a plan of action for multi-priority control is required. In this paper, we propose a method for formation-collision co-awareness by adapting the thin-plate splines algorithm to minimize deformation of the swarm's formation while avoiding obstacles. Furthermore, we use a non-rigid mapping function to reduce the lag caused by such maneuvers. Simulation results show that the proposed methodology maintains the desired formation very closely in the presence of obstacles, while the response time and overall energy efficiency of the swarm is significantly improved in comparison with the existing methods where collision avoidance and formation control are only loosely coupled. Another important result of using non-rigid mapping is that the slowing down effect of obstacles on the overall speed of the swarm is significantly reduced, making our approach especially suitable for time critical missions.
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Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2017.DOI
Energy-efficient Formation Morphing for
Collision Avoidance in a Swarm of
Drones
JAWAD N. YASIN1, SHERIF A.S. MOHAMED1, MOHAMMAD-HASHEM HAGHBAYAN1, JUKKA
HEIKKONEN1, HANNU TENHUNEN2, MUHAMMAD MEHBOOB YASIN3AND JUHA PLOSILA1
1Department of Future Technologies, University of Turku, 20500, Finland
2Department of Electronic Systems, KTH Royal Institute of Technology, Stockholm, 11428, Sweden
3Department of Computer Networks, College of Computer Sciences & Information Technology, King Faisal University, Hofuf, Saudi Arabia
Corresponding author: J. N. Yasin (e-mail: janaya@utu.fi).
This work has been supported by the Academy of Finland-funded research project 314048.
ABSTRACT Two important aspects in dealing with autonomous navigation of a swarm of drones are
collision avoidance mechanism and formation control strategy; a possible competition between these two
modes of operation may have negative implications for success and efficiency of the mission. This issue
is exacerbated in the case of distributed formation control in leader-follower based swarms of drones since
nodes concurrently decide and act through individual observation of neighbouring nodes’ states and actions.
To dynamically handle this duality of control, a plan of action for multi-priority control is required. In
this paper, we propose a method for formation-collision co-awareness by adapting the thin-plate splines
algorithm to minimize deformation of the swarm’s formation while avoiding obstacles. Furthermore, we
use a non-rigid mapping function to reduce the lag caused by such maneuvers. Simulation results show that
the proposed methodology maintains the desired formation very closely in the presence of obstacles, while
the response time and overall energy efficiency of the swarm is significantly improved in comparison with
the existing methods where collision avoidance and formation control are only loosely coupled. Another
important result of using non-rigid mapping is that the slowing down effect of obstacles on the overall speed
of the swarm is significantly reduced, making our approach especially suitable for time critical missions.
INDEX TERMS Autonomous aerial vehicles, Collision avoidance, Multi-robot systems, Formation
maintenance, Swarm intelligence, Leader follower
I. INTRODUCTION
RESOURCE utilization and decision making optimiza-
tion in autonomous navigation for a swarm of robots is
gaining traction in the research community [1]. The motive
for this is the absence of a multi-objective strategy in the
traditional operation of robots, e.g., drones/UAVs, for opti-
mally or near-optimally achieving various system goals under
various mission or design constraints such as the flight time
and energy payload [2], [3].
Swarms of drones have demand in vast and diverse ap-
plication areas for instance in the military, commercial use,
search and rescue, monitoring traffic, threat detection espe-
cially at borders, and atmospheric research purposes [4], [5].
Due to the ability to work in a collaborative manner in a 3-
dimensional space, research on optimal navigation of swarms
is gaining even more attention in the research community [6].
The deployment of an efficient navigation system for swarms
or multiple UAVs adds significant research challenges over
single UAVs. Two important raised challenges while focusing
on navigation in a swarm of drones are: 1) the formation and
its maintenance and 2) collision avoidance [7], [8]. Collision
avoidance primarily focuses on path planning of individual
drones to steer clear of possible collisions between the drones
themselves within the swarm and between drones and exter-
nal obstacles in the environment [8]. The responsibility of
formation algorithms, in turn, is to define the location of each
drone with respect to the other drones [9].
The interdependence of formation control and collision
avoidance is of significant importance as collision avoidance
needs to be considered in order to maintain the formation, and
similarly, in order to avoid collisions, the intended formation
needs to be considered. In the decision making for both
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processes, the stabilization time and energy consumption
minimization should be considered. Mainly a swarm deviates
from the formation for collision avoidance, i.e., to avoid an
obstacle, and after passing the obstacle the swarm turns back
again to the formation. This sequential process of deviation
and turning back must be safe, fast, and energy-efficient.
Several unanticipated parameters or factors may affect the
optimal implementation of collision avoidance along with a
dynamic formation control algorithm. For instance, a change
in the formation may be forced by prioritizing collision
avoidance over formation maintenance due to unaccounted
objects/obstacles or narrow gaps/openings between multiple
obstacles. In order to do the whole process autonomously,
we need to analyse how collision avoidance and formation
control can be systematically integrated together. In this
paper, the proposed algorithm considers these factors by
taking into account the strategy of maintaining the swarm
formation dynamically with variable speeds of UAVs along
with an efficient collision avoidance methodology. To make
it safe, each drone should obey a maximum possible distance
from the obstacle and other drones. To make it fast and
energy-efficient, the shortest spatial deviation and turning
back should be considered. In our proposed method, the
deviation phase follows reflexive decision making due to
the uncertainty of the obstacle. The main objective is to
reduce the spatial deviation while keeping a safe distance.
For the turn back phase, we propose an energy function
for the swarm formation inspired by the energy function
of a thin-plate spline, where the result of minimizing this
energy function, determines the navigation decision for each
drone to resume the formation. Our approach focuses on
integrating all these features together along with reducing
the total energy of the system. Once these factors have been
taken into account, and the pattern has been developed for
switching between the formation maintenance and collision
avoidance modes autonomously, the thin-plate splines tech-
nique is integrated into the algorithm in order to optimize
it further by reducing the overall energy of the system.
This technique helps by optimally reducing the disturbances
caused by obstacle(s) by bringing the node(s)1or UAVs back
to their stable coordinates in a timely yet aggressive manner.
The contributions of this paper compared with our previ-
ous paper and the state-of-the-art are listed as follows:
1) Proposing a new idea to reduce the time and energy
through random dispersion of drones in the first phase
of detecting an obstacle.
2) Proposing a new idea to reduce the time and energy by
applying the thin-plate splines algorithm in the second
phase of detecting an obstacle.
3) Providing comprehensive simulation results for a
swarm of drones for the proposed idea and implement-
ing recent existing methods to show the efficiency of
our technique in comparison with those ideas.
1Terminologies UAVs, drones, and nodes are used interchangeably in this
paper.
The rest of the paper is organized as follows. Section
2 covers the related work. In Section 3, basic concepts of
formation, swarm, and collisions are briefly described. The
proposed algorithm and its development is given in Section
4. Optimal swarm reconfiguration is explained in Section 5.
Section 6 focuses on simulation results and related discus-
sion. Finally, concluding remarks are presented in Section 7.
II. RELATED WORK
Formation control algorithms can be categorized into three
general approaches [10], [11], namely: 1) the virtual structure
based approach, in which all the drones in the swarm forma-
tion are navigated as if there was a single big drone and hence
the same trajectory is taken [12], [13]; 2) the leader-follower
based approach, where every drone functions individually
and autonomously by calibrating or altering its position
according to the leader and maintaining its position in the
formation as close as possible to the desired coordinates [14],
[15]; and 3) the behaviour based approach, in which based on
a pre-defined strategy the drone selects one of the multiple
behaviours [16], [17]. The leader-follower based approach
is more common out of the aforementioned approaches, due
to its ease of analysis and implementation [18], [19]. In this
approach, leaders are explicit, and it is assumed that all or
some of the followers have access, when required, to relevant
motion information such as velocities and positions of the
leaders within their sensing range [20], [21].
With the integration of commercial, leisure based and
military UAVs and/or aircraft, a good collision avoidance
algorithm or system becomes exponentially important for
their safe operation in the civilian airspace [22]. During the
flight, they can encounter both stationary and moving obsta-
cles and objects that need to be safely and reliably evaded
using the collision avoidance system [23], [24]. Typically,
algorithms for collision avoidance can be divided into three
generic classes [25], [26]: 1) force-field methods that work on
the principle of applying attractive/repulsive electric forces
existing amongst charged objects; each drone in a swarm
is considered a charged particle, and attractive or repulsive
forces between drones and the obstacles are used to generate
and choose the routes to be taken [27], [28]; 2) sense-and-
avoid based methods, where the process of collision avoid-
ance is simplified into individual detection and avoidance of
the objects and obstacles, resulting in short response times
and reducing the computational power needed [29], [30];
and 3) optimization based methods which focus on providing
the optimal or near-optimal solutions for path planning and
motion characteristics of each drone with respect to the other
drones and obstacles. In order to calculate efficient routes
within a finite time horizon, these methods rely on static
objects with known locations and dimensions [31], [32].
In formation flight, UAVs/nodes perform varying ma-
neuvers like accelerating, decelerating, synchronized move-
ments, and turning in different directions, that require each
member of the formation to have a specific minimum dis-
tance from other members. To successfully perform those
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maneuvers and missions, nodes must have the ability to avoid
collisions with other nodes in the swarm and with external
obstacles [27], [33].
Basically, the collision avoidance process while keeping
the formation consists of two main phases, i.e., 1) reforming
the swarm to avoid a collision while approaching an obstacle
and 2) resuming the formation after passing the obstacle.
Most of the existing works completely lack such tight in-
tegration of dynamic formation maintenance and collision
avoidance strategies. They either focus on keeping the forma-
tion or avoiding collisions based on state-of-the-art collision
avoidance algorithms. In our proposed methodology, we in-
tegrate dynamic formation maintenance along with collision
avoidance capabilities for swarms to address an important
research topic not properly covered by the state-of-the-art.
For formation control of the swarm, we utilize the leader-
follower based approach due to its ease of implementation,
analysis, and scalability [20], [23]. The objective of our
approach is to reduce the collision avoidance time and energy
consumption during the reformation and resuming processes.
During this formation morphing, the leadership of the swarm
might be totally changed (as shown in Figure 1), and an
ex-follower drone may take the role of the leader, further
highlighting the novelty of the proposed method with respect
to the state-of-the-art. It is important to note here that the
overlapping of the UAV1 and UAV2 (shown as blue and
green paths) is at different times, that is due to the fact as
soon as UAV 2 detects UAV1 coming in front of it to bypass
the obstacle, UAV2 slows down to maintain safe distance
with UAV1 while maintaining its own trajectory for obstacle
avoidance. As shown in the figure, UAV3 had minimum
deviation and did not have to slow down as much, it may
bypass the obstacle before UAV1 (the original leader), and
hence UAV3 may take the role of the new leader as shown in
Figure 1.
FIGURE 1: Formation and collision avoidance
III. PRELIMINARIES
This section describes the basic concepts essential for the
work presented in this paper.
Swarm robotics can be defined as the study of how a
system consisting of multiple collaborating robots can be de-
signed by analyzing the local interactions between the robots
themselves and the robots and their environment [34]. It is
strongly inspired by real-life phenomena such as swarms of
insects and flocks of birds. It is also referred to as distributed
robotics [35], robot colonies [36], and collective robotics
[37].
Aformation in swarm robotics refers to a desired arrange-
ment of the robots in a swarm, a particular arrangement or
shape of positions the multiple robots aim to maintain with
respect to each other. The swarm can be ordered to maintain
a certain shape of formation to perform a given mission [38].
In a queue formation, drones or robots form a simple line or
sequence, following each other and maintaining the distance
between each other within a given range. Its key benefit is
that it enables a swarm to pass through obstacles without
breaking the formation. Any arbitrarily shaped formation
may have to reorganize itself into a queue formation in
order to avoid and navigate through multiple obstacles while
maintaining connectivity and tracking between the nodes.
A drone is defined to have a collision with an object, i.e.,
another drone within the swarm or an external obstacle, if the
distance of the drone to the object is less than a predetermined
collision radius,Rc. Expressing this mathematically, a colli-
sion is considered taking place when the following condition
is true:
||ruro|| < Rc(1)
where ruand roare the position vectors of the UAV and the
object, respectively.
Similarly, an obstacle is detected by a drone, when the
following condition holds:
||ruro|| < dRange (2)
where dRange is the detection range radius of the UAV,
which varies and is dependent on the characteristics of the
on-board sensor system.
For ease of simplicity, the following assumptions and
initial conditions are used in this study:
1) All obstacles are stationary and/or can be introduced in
front of the UAVs at any given time.
2) UAVs have variable speeds and accelerate or decelerate
as needed. Using an on-board sensor system, every
UAV obtains its own position and velocity vectors.
The on-board sensor system could include lidar, sonar,
radar, and GPS to mention a few.
3) There is no information loss in the communication
channels between the UAVs.
IV. THE PROPOSED APPROACH
In this section, we describe the proposed Energy-efficient
Formation morphing for Collision Avoidance (EFMCA) al-
gorithm for a swarm of drones. The overall strategy is to
combine swarm formation control and collision avoidance
mechanism to facilitate the process of autonomous swarm
navigation, Figure 1. To accomplish this, a novel top-level
algorithm is developed, composed of two partial feedback-
based algorithms: one for formation control and one for
collision avoidance. The feedback for each drone’s controller
comprises both collision radius and formation distance, and
the goal is to minimize their errors, i.e., differences between
the observed values and the reference values. The angular
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error is the difference of the required angle from the observed
angle, indicating how much the node should turn to maintain
its position w.r.t. its neighbour. Correspondingly, the distance
error is the difference of the measured distance from the
reference distance, indicating how much the node should get
closer or farther to or from its neighbour.
If there is no feedback for an object detected by the on-
board sensor system, indicating there is no external object
in the vicinity, the algorithm maintains the formation by
dynamically checking and adjusting the distance of the drone
to its neighbours. The goal is to keep the distance greater than
the collision radius and close to the pre-specified formation
distance.
Upon detection of an obstacle, the algorithm raises the pri-
ority of the collision avoidance part. The collision avoidance
part of the algorithm gets the highest priority once the UAV
approaches the minimum safe distance from the obstacle.
After bypassing the obstacle(s), a Failsafe/Fault-Tolerance
check is executed to see if the UAV has lost its connection
or if it still has a connection with its respective leader.
A. FORMATION-COLLISION CO-AWARENESS
Algorithm 1 gives the general pseudo-code of the top-level
formation-collision co-awareness algorithm. As our initial
setup, we presume that the UAVs are spawned at random
coordinates, and also the IDs to the nodes/UAVs are assigned
before the mission is started. Every node executes this top-
level algorithm locally by deploying the algorithm on its on-
board processing unit. The path planning of the leaders and
the navigation of the swarm is out of the scope of this work.
Formation maintenance is initiated based on the feedback
on the distance the node has to its neighbours (Line 2 in
Algorithm 1). Then Eformation, i.e., the formation error, is
calculated. To achieve this, a threshold value is added to the
absolute value of the relative angular and distance position of
a drone with respect to its neighbours (Line 4). The degree
of freedom that each drone can have in the formation of the
swarm is determined by the threshold value. Depending on
whether an object is detected or not, the formation error is
processed accordingly. In case of an observed obstacle, i.e.,
the obstacle comes within the detection range, the collision
error is calculated, specifying the difference between the
obstacle distance and the collision radius (Line 5).
There are three cases on which the algorithm works
(Lines 6-13). If there is a positive formation error, i.e., 0<
Eformation, but no probable obstacle in the vicinity, then,
in order to decrease the error, the algorithm utilizes the
Formation function to reconfigure the relative angular and
distance positions of the drones (Lines 8-9). The Collision-
aware formation function is executed in the case where an
obstacle is detected by the sensors, but there is no immediate
danger of a collision. Then the formation of the swarm is re-
configured by considering the location of the obstacle under
observation (Lines 10-11). However, the Collision avoidance
function is launched, if the condition 0< Ecollision is true
indicating the obstacle is too close to the drone (Lines 12-
13). This operation is oblivious of the formation, meaning
that formation protocols are completely ignored; only the
distance of the drone w.r.t. the obstacle matters. In this mode,
only Collision avoidance of the above three functions can be
executed; the two formation-adjusting functions are disabled,
independently of the value of Eformation .
Once a collision has been avoided successfully, the control
is transferred to the Turn-Back function to minimize the
disturbance caused by the evasive maneuvering, i.e., to bring
the nodes back into the formation as efficiently as possible
(Lines 16-17). Since the disturbance caused by collision
avoidance might totally reform the swarm, this process might
be accompanied by selecting a new leader for the swarm. As
a fail-safe check, i.e., a special scenario in case the leader
is lost or undetectable by the follower, the follower drone
temporarily sets itself as its own leader, broadcasts this to
its followers, and starts navigating towards the destination
(Lines 19-20). However, as soon as the leader is detected, i.e.,
gets back in the visible range, the drone immediately comes
back into the formation and the starts to follow the leader
(Lines 21-22). All the functions in Algorithm 1 are explained
in detail in the following subsections.
Algorithm 1 Formation-collision co-awareness
procedure FORMATION -COLLISION CO-AWARENESS
2: formation Initiate Formation;
while True do
4: Efor mation Calculate distance and angular formation error
(formation);
Dobstacle,Ecollision Calculate obstacle distance and collision error
if any;
6: ST AT E (0 < Efor mation, Obstacle is probe-able by local sensors,
0 < Ecollision);
switch ST AT E do
8: case (True, False, False)
Formation (Eformation );
10: case (-, True, False)
Collision-aware formation (Eformation ,Dobstacle );
12: case (-, -, True)
Collision avoidance (Ecollision);
14: T P S_F lag = True;
end switch
16: if TPS_Flag == True; then
Turn-Back(T P S_F lag);
18: end if
if My Leader is out of range then
20: My Leader Self ;
else
22: My Leader Leader(Self );
end if
24: end while
end procedure
B. FORMATION ALGORITHM
Algorithm 2 Formation
procedure FORMATION ( (Edistance ,Eangular )Ef ormation )
2: (distanceErr or,angularE rror)Rformation Ef ormation
if 0< ABS(distanceE rror )then
4: Calculate Distance From Respective Leader;
Accelerate/decelerate Accordingly;
6: end if
if 0< ABS(ang ularEr ror)then
8: Set Angular Direction (Rangular );
end if
10: end procedure
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A unique ID that is given to each node in the swarm,
is used by the other nodes and the leader for recognition
purposes. Then the leader starts navigating towards the des-
tination; in the meantime, the followers try and maintain
the formation by keeping the required distances from the
respective neighbours. The general pseudo-code of the for-
mation function is given in Algorithm 2. The input of the
algorithm comprises the pre-specified formation information
that is considered the reference, i.e., Rformation (consisting
of the reference distance Rdistance and angle Rangular ),
and the instantaneous captured formation information, i.e.,
Eformation, that is the estimated distance and angle each
drone has w.r.t. its neighbours (e.g. the leader and follower
in a queue formation) at a given time. First, the deviation
of each drone w.r.t. its pre-defined position is determined
by calculating the angular and distance errors (Line 2 in
Algorithm 2). The algorithm then starts to change the state of
the swarm by manipulating the node’s mechanical actuators,
in the case the angular or distance error is greater than the
defined threshold indicating that the variation is significant
and affects the formation negatively. The distanceError is
calculated as follows:
distanceErr or =q(LxFx)2+ (LyFy)2(3)
where Fx,Fyand Lx,Lyare, respectively, the follower’s
and leader’s x and y-coordinates. If the distance error is
positive, indicating that the distance between the node and its
neighbour is too high, the drone accelerates to catch up and
attain the desired formation distance. Similarly, in the case
of a negative distance error, meaning that the distance of the
node to its neighbour is too low, the drone starts to decelerate
in order to decrease the absolute value of the distance error.
To maintain the desired distance and orientation, each drone
employs a local speed control for the possible manoeuvres.
Each follower determines the angle of the leader as shown
in Figure 2 and calculates as follows:
Angle(y, x) =
arctan(y
x)x > 0,
arctan(y
x) + π x < 0and y 0,
arctan(y
x)π x < 0and y < 0,
+π
2x= 0 and y > 0,
π
2x= 0 and y < 0
(4)
FIGURE 2: Distance and Direction Calculation
The result is always between -πand π. Using the plane
vector from the origin to the target, the angle is formed w.r.t.
the positive X-axis. Since the signs of both inputs are known
and taken into consideration, the correct quadrant of the
computed angle, i.e., angularError, and the corresponding
direction values are calculated by using the result from the
above equation as follows:
angularE rror = (dx =cos(Angle), dy =sin(Ang le)) (5)
C. COLLISION-AWARE FORMATION ALGORITHM
Algorithm 3 Collision-aware Formation Algorithm
procedure COLLISION-AWARE FORMATION(Eformation , Dobstacle )
2: newT emporary F ormation determineNewFormation (
Efor mation, Dobstacle );
Formation (newT emporary F ormation);
4: end procedure
If it is not possible to maintain the formation due to the
detection of an obstacle by one of the nodes, Algorithm 1
calls the proposed collision-aware formation function. This
function is specified in Algorithm 3. The main plan of action
in situations, where Dobstacle (obstacle’s distance) is within
the range of a node but not small enough to justify the actual
collision avoidance measures, is to reshape the formation
while symmetrically shifting the swarm at the same time in
order to divert the observer node, and thereby its followers,
from the potential collision course. Based on this, the algo-
rithm first determines a new formation which is close to the
original one, making it easier to bypass the obstacle (Line 2 in
Algorithm 3). After this decision, the information regarding
the new formation is fed to the formation function in order
to reshape the swarm (Line 3). Then the obstacle distance
and the collision error are recalculated in the next iteration
of Algorithm 1 to check if the obstacle is still within the
detection range of the observer node or not. If the obstacle is
outside the detection range of the node, the formation returns
back to the original one (Lines 8-9 in Algorithm 1).
D. COLLISION AVOIDANCE ALGORITHM
The pseudo-code of the collision avoidance function is shown
in Algorithm 4. Collision avoidance function is invoked if an
obstacle is encountered critically close to the node. First, it
starts to detect the edges of the obstacle, at which point the
angles between the node’s and obstacle’s positions as well as
the exact position of the obstacle can be determined (Line 3
in Algorithm 4). If the edges of the obstacle are in the visible
range of the on-board sensor(s), it is checked if there is only
one obstacle or multiple obstacles in the vicinity (Lines 4-
5). In the case of multiple obstacles, the gap between the
obstacles is calculated as shown in Figure 4(a) (Line 6). Then
the algorithm checks and decides, based on the calculations,
if it is safe and possible for the drone to go through the
detected gap (Lines 7-8). If the gap is not wide enough for
the drone to go through, the algorithm treats the obstacles as
a single entity and guides the drone around the obstacles to
avoid collisions (Lines 9-11). Moreover, if only one obstacle
is detected (Line 13), the short-term path planning is done
accordingly by calculating in which direction the node should
navigate to bypass the obstacle with minimal deviation from
its original path (Lines 13-14). However, in case neither edge
of the obstacle is visible/detected by the on-board sensor
system of the drone (Line 17), a tangent line is drawn from
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the drone’s current position to the destination coordinates,
and the path is chosen accordingly by navigating towards
the destination while avoiding colliding with the obstacle and
staying as close to the tangent line as possible (Lines 18-19),
see Figure 4(b). The value of Ecollision is updated to check
for successful collision avoidance (Line 21).
Algorithm 4 Collision Avoidance Algorithm
procedure COLLISION AVOI DANC E(Ecollision )
2: while 0< Ecollision do
edges detect edges ();
4: if edges contains visible edges then
if More than one obstacle is detected then
6: Dsafe Calculate gap between obstacles (edges);
if Dsafe >Rcthen
8: Short-term path planning (edges); .Align UAV to pass
through the obstacles
else
10: pathP lan Calculate path plan (edg es);
Short-term path planning (pathP lan);
12: end if
else
14: pathP lan Calculate path plan (edg es);
Short-term path planning (pathP lan);
16: end if
else
18: tangentLine Calculate tangent line();
Short-term path planning (tangentLine);
20: end if
Ecollision Update collision error;
22: end while
end procedure
FIGURE 3: Obstacle Detection and Avoidance using geomet-
ric guidance law
To put in a nutshell, the proposed collision avoidance
function, i.e., Algorithm 4, operates based on three different
cases, namely: 1) there is a single obstacle in the vicinity and
its edges are detected, Figure 3; 2) there are multiple obsta-
cles and their edges and gaps are detected, Figure 4(a); and
3) the edges of the obstacle(s) are not visible, indicating the
obstacle is very large; in this scenario, the path is determined
based on a tangent line, Figure 4(b). If Dobstacle, i.e., the
distance from the drone to the obstacle, is within the middle
ground of the detection range and safe distance fs(Table 1,
Figure 3), the algorithm starts decelerating the drone while
calculating the angle at which the detected obstacle lies in
order to deviate from that path. The collision avoidance
algorithm takes complete control of the system as soon as
Dobstacle gets closer to fsand guides the drone to go around
the obstacle safely.
TABLE 1: Description of Variables from Fig.
Variables Description
duUAV’s width
fsminimum safe distance allowed from
from either side of UAV
h1detected distance of the object’s edges
h2on the left and right sides
a1calculated from the centre of the UAV,
linearized distance of the object on the left
a2and right side of the UAV respectively
d1linearized distance of the object straight
d2ahead of the UAV
P1point where the edge(s) (if any) were
P2detected by the on-board sensor
θ1angles of the edges
θ2
φ1linearized angle
The situation in which the edges of a single obstacle are
detected by the nodes is illustrated in Figure 3. Table 1 lists
the used variables and their explanations.
All possible combinations of the object’s location are
analysed once the exact coordinates of the obstacle have been
calculated, and the decision is made accordingly. It is then
decided by the algorithm if it is safe to continue along the
current path or if the drone must be diverted to a certain
extent to avoid colliding with the object. For instance, if a2
< (du/2)+fs(in Figure 3), the algorithm reroutes the drone to
left from its current route as continuing along the same path
may result in a collision with the obstacle on the right side of
the drone. However, in case a2(du/2)+fs, no rerouting or
deviation from the original path is needed due to the fact that
the obstacle is on the right side of the drone and is not in the
critical collision radius.
Furthermore, upon detecting multiple obstacles and their
corresponding edges, two different actions can be performed,
i.e.: 1) extending the collision envelope when Dsafe Rc,
and 2) activating the detection and gap calculation mode
when Dsafe > Rc. Here the distance between the inner
edges of the obstacles is indicated by Dsafe and the collision
radius is denoted by Rc. Based on action 1, both obstacles
lying in close proximity are considered a single entity, by
extending the collision envelope, while calculating the avoid-
ance maneuver parameters (Lines 9-10 in Algorithm 4). In
this case, as shown in Figure 4(a), θ1L and θ2R are taken
into account due to the fact that both obstacles are treated
as a single obstacle. Then the calculations are performed to
bypass the combined obstacle by flying from either side (left
or right) of the obstacle.
In the latter case, i.e., the action 2, the algorithm analyses
the detected gap between the obstacles to determine if the
width Dsafe satisfies the condition Dsafe 2fs+du, where
duis the width of the drone and fsis the safe distance
(Table 1, Figure 3), indicating that the opening/gap between
the obstacles is wide enough for the drone to go through
them. However, if the condition is not satisfied, it indicates
that it is physically not possible for the drone to go through
the gap between the obstacles, i.e., the gap between the
obstacles is too narrow and smaller than the width of the
drone and hence does not provide sufficiently large safety
margin. Subsequently in this case, the algorithm switches
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(a) Multiple Obstacles with opening between them
(b) Local decision making in case of unknown
length of obstacle
FIGURE 4: Multiple Objects and Local decision making
Figures
back to the action 1, i.e., instead of considering the angles θ1R
and θ2L like in the action 2, the algorithm opts for the angles
θ1L and θ2R (Figure 4(a)), and the obstacles are regarded as a
single obstacle which is then bypassed either from its left or
right side.
In the scenario where the obstacle extends beyond the vis-
ible range of the on-board sensor system and its dimensions
cannot be computed, the algorithm uses the data provided by
the local GPS unit to draw a tangent line to the destination,
that is the line defining the shortest path between the drone
and the destination, see Figure 4(b). The node, based on the
angle of the tangent, decides which direction it should opt
for. For example in Figure 4(b), in order to select from the
only possible choices that are west/left or east/right, using the
angle of the tangent line, it is determined that the destination
is towards the north-west of the drone. Consequently, to avoid
the obstacle and to stay as close to the tangent line as possible
while keeping the minimum safe distance from the obstacle
for safe maneuvering, the green path is chosen.
V. OPTIMAL SWARM RECONFIGURATION
After observing an obstacle in its flight path, a UAV needs
to maneuver around it according to rules set by the collision
avoidance algorithm. Such maneuvers generally distort the
shape of the swarm’s formation from the originally planned
shape that may, sometimes, be crucial to the success of its
mission. It is the intent of our submission to continually
guard the collision avoidance maneuvers such that the dis-
turbance from the planned, i.e. optimal, formation is kept at
the minimum during the course of the maneuver(s) and that,
after navigating past the obstacle(s), the swarm is returned
back to its initial formation. This process raises a formation
construction problem that is widely covered in the literature
[4], [39]. However, in our case, the formation algorithm, or
in other words the disturbance rejection of a swarm, must
be compatible with our obstacle avoidance algorithm whose
main target is to reduce the overall settling time and energy of
the system. It is worth mentioning that we deploy a non-rigid
mapping function for efficiency reasons. That is to say that
the process of returning the swarm formation to its original
shape is not required to re-establish initial neighbouring
states among the drones since all the drones are considered
to be identical. For example, in the original state drone 2
has two neighbours drones 1and 3, after reconstructing the
formation its new neighbours may be drones 4and 5, it may
even become the new global leader. In the following text, we
refer to the original i.e. the desired formation shape as the
model formation, while the shape at any instant during the
flight is referred to as the scene. In the process of returning
from the scene to the model, there are two main questions
to be addressed. Firstly, what is the optimal alignment of
nodes in the scene to node positions in the model? We name
this as the mapping problem. Secondly, what is the optimal
trajectory of each node in the scene so that it is mapped into
the desired node position in the model? For the first issue,
we apply the well-know concept of point set registration
[40]–[42], which is based on thin-plate splines formulation
(TPS) that is commonly used to solve data interpolation and
smoothing problems [43]. After determining the mapping
strategy, for the second problem, the proposed collision
avoidance algorithm utilizes the shortest path scheme for
deciding trajectories of individual nodes. Though a more
efficient solution for the second part may be possible, our
current focus is on designing an optimal mapping strategy,
thus, it suffices to indicate, here, that search for an efficient
trajectory of each node is one avenue for future work. In the
following, we first explain the concept of thin-plate splines
(TPS), and then we propose an algorithm based on the same.
A. THIN-PLATE SPLINES (TPS)
A spline is a function defined by polynomials in a piece-
wise manner. Spline curves are popular and are used for
approximation of complicated shapes via curve fitting due to
their ease of use and non-complicated construction [43]. We
analyse the algorithm in 2D to make it simpler; consequently,
two sets of correspondence points, i.e., data sets, are assumed
Xi.e. xi,i=1,2,3,...,nand Vi.e. vi,i=1,2,3,..
. , n. Here, the locations of a point in the scene and model
are given by xiand virespectively, where xi= (1, xix,
xiy) and vi= (1, vix ,viy ). A mapping function, i.e., f(vi),
can be acquired while keeping the shape of the disturbed
formation/function under consideration, by minimizing the
energy function, ETPS, given by the following equation:
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Yasin et al.: Energy-efficient Formation Mor phing for Collision Avoidance in a Swarm of Drones
ET P S (f) =
n
X
i=1
||xif(vi)||2+
λZZ [( 2f
∂x2)2+ 2( 2f
∂x∂ y )2+ (2f
∂y2)]dxdy
(6)
The amount of formation disturbance is evaluated by the
energy function ET P S . The scaling factor is denoted by λ.
If we do not intend to keep the shape of the disturbed swarm
under consideration and only intend to map one point set over
the other, we set λto zero then only the closest points are
mapped without the shape being considered. When the λis
set to zero, ET P S , i.e., disturbance, is given by:
ET P S (f) =
n
X
i=1
||xif(vi)||2(7)
The mapping of points to the corresponding point sets
while considering the intended formation is represented by
the integral part of the equation. The mapping process from
the highest point in disturbance formation to the original
formation shape, i.e., the scene and the model, is determined
by minimizing of the temperature function. Once the desired
mapping is calculated, each drone in the scene starts follow-
ing the shortest path to reach its hypothetical position in the
model.
B. TURN-BACK FUNCTION
Algorithm 5 Turn-back
procedure TURN-BAC K (TPS_Flag )
2: while TPS_Flag == True do
FLocation = Determine the future location of the swarm;
4: Determine the new coordinates for each drone;
Temperature function minimization: TPS(FLocation);
6: if All nodes REAC H new coordinates then
TPS_Flag False;
8: end if
end while
10: end procedure
Algorithm 5 gives an overview of our TPS-based turn-back
function. First, the future location of each node in the swarm
is determined based on the current location of the nodes (Line
3). Based on each node’s location, the new coordinates are
determined for each drone (Line 4). Next, these values are fed
to the TPS-based temperature minimization function, to bring
the drones to their new coordinates as optimally as possible
(Line 5). Once all drones have reached their respective new
coordinates (Line 6), TPS_Flag is set to False and the control
is returned to the main function (Line 7).
Figure 5 shows the example scenario where the swarm
comes across an obstacle and starts reshaping formation
while avoiding collision with the obstacle. Figure 5(a) shows
the initial phase of formation and the locations of all the
drones at the starting point. Figure 5(b), shows the distorted
formation and the locations of the drones at halfway stage.
In order to avoid the obstacle, UAV1 (red) had to slow down
and deviate from its original path, thus, it comes in front of
UAV2 (green). As soon as UAV2 detects UAV1 in its way,
it slows down to maintain safe distance from objects ahead
of itself. Whereas UAV3 (blue) needs only a small deviation
from its original path, thus, it gets ahead of the rest of the
formation and becomes a candidate for going to the position
of UAV1 instead of slowing down in order to retain its earlier
position in the model. UAVs 4 and 5, i.e., pink and grey
respectively, maintain their own trajectories as they never
came within colliding range of the obstacle. Figure 5(c),
shows the final reformation after collision avoidance. After
successfully avoiding the collision, in the reformation phase,
UAV3 moves to the original position of UAV1 in the model,
while UAV1 moves to the previous position of UAV2 and
UAV2 moves to the position which was originally occupied
by UAV3; all the while utilizing the shortest path to reach
their respective final locations.
VI. SIMULATION & RESULTS
Simulation setup is as follows:
area defined for simulations was setup as 700 X 500m
2D-XY plane
all the UAVs are at the same altitude
UAVs fly in horizon (self-leveling) mode instead of
space mode, since horizon mode offers stabilized flight
as the drone will self-level utilizing gyro and accelerom-
eter
five UAVs are launched from random locations in close
proximity
unique IDs are assigned to each UAV, incrementally
from 1 to 5
a simple queue formation is chosen whereby each UAV
follows its immediate leader, while UAV with ID = 1, is
chosen as the global leader
The point mass particle model is used for simulating and
visualizing the UAVs. By keeping the vertical axis constant,
the UAVs navigate only in the XY-plane. Therefore, the equa-
tions of motion applicable for a point-mass particle moving
in a 2D space are utilized here, and thus 6dof movements
are not considered in this work. Based on this, the dynamics
of the drone utilized in this work is only the mass of the
drone that has some initialized velocity vector and change
in the velocity, i.e., acceleration. Furthermore, it is important
to note here that algorithm is not restricted for rectangular
objects as it mainly depends on the perception precision of
the drone. Similarly, it can be perceived as during the percep-
tion phase, each obstacle is encapsulated into a bounding box
and the algorithm takes into consideration those bounding
box. Increasing the precision of the perception, refines the
bounding box shape closer to the actual shape of the detected
obstacle.
Upon spawning, UAV1, the global leader, starts navigating
towards the destination, whereas the rest of the UAVs start to
maintain the desired formation by accelerating/decelerating
to reach their desired positions and maintain the distance
from their respective leaders. To summarize, each UAVi+ 1
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Yasin et al.: Energy-efficient Formation Mor phing for Collision Avoidance in a Swarm of Drones
(a) Formation at beginning (b) UAVs bypassing obstacle by keeping safe
distance (c) Final Place of each deviated drone, with
new locations in the formation
FIGURE 5: Flexible formation through obstacle scenario
(a) UAVs forming Queue Formation
(b) UAVs in queue formation bypassing obstacle
by keeping safe distance
FIGURE 6: UAVs at random coordinates coming into for-
mation by finding their respective leaders and bypassing an
obstacle. Here, the solid circle in the center of each drone
shows the Collision Radius, the outer hollow circle depicts
the Detection Range and the arrow indicates the direction of
movement
starts to track and follow UAVi, where i= 1,..,4. Figure 6
shows the scenario where five UAVs are spawned at random
coordinates in close proximity and come into formation by
finding their respective leaders. The positions and move-
ment/trajectories of the drones upon deployment and during
early stages of queue formation are depicted in Figure 6(a).
The situation emerging soon after the first obstacle, namely
Obstacle A, comes within the visibility range of the leader
is shown in Figure 6(b). Here, the leader navigates along the
obstacle by keeping safe distance from it following Algorithm
4, the remaining UAVs follow the leader while maintaining
the formation and keeping the safe distance from the obstacle
as well, as per Algorithm 3.
The trajectories of the drones while maintaining the forma-
tion and navigating through multiple obstacles are illustrated
in Figure 7. The situation whence the main leader observes
the second obstacle, namely Obstacle B, while traversing
along obstacle A is shown in Figure 7(a). Since there are
two obstacles with a large enough gap between them, the
swarm’s leader decides to go through the space between the
two obstacles, and the other UAVs follow the leader (multiple
obstacles case in Algorithm 4). Notice that in such a situation,
the shape of the queue formation is not a rigid line. Instead,
the drones reshape the formation into a bent/arched line e.g.
when passing between the obstacles, and return to a straight
line formation when they have passed the obstacles. This
demonstrates the robustness and agility/adaptability of the
proposed algorithm. The reformation process after coming
out of the obstacles and next to the destination is shown in
Figure 7(b).
An interesting situation, namely, the lost drone scenario
is illustrated in Figure 8, where one of the drones wanders
too far off from its immediate follower. Basically, it moves
past the obstacle before other drones come into formation
and it is, therefore, not in the range of its follower drone
In the instant scenario, the global leader, namely UAV1, is
hidden by an obstacle, therefore, its follower, namely UAV 2,
loses connection to it. Now, till such time that UAV1 comes
in the visible range of UAV2, the rest of the swarm continues
its journey toward the destination with UAV2 as the tempo-
rary leader, as shown in Figure 8(a). When UAV1 becomes
again visible to UAV2, Figure 8(b), the swarm immediately
resumes the original formation and UAV2 and its followers
accelerate towards the original leader UAV1. If UAV1 re-
mains invisible/lost, UAV2 and its followers continue their
journey without UAV1 until they reach the destination.
In order to analyse the efficiency and the performance
of the proposed algorithm, we report and compare some
acquired measurements of the system that is based on our
first experiment as shown in Figure 6(b) above.
The velocity of each UAV and the relative distance be-
tween each UAV and its respective leader are shown in Figure
9. It is evident from the figure that, after the warm-up phase,
the relative distances and velocities remain within close range
VOLUME 4, 2016 9
Yasin et al.: Energy-efficient Formation Mor phing for Collision Avoidance in a Swarm of Drones
(a) UAVs in formation going through opening
between obstacles
(b) UAVs coming out of the obstacles and reach-
ing the destination point
FIGURE 7: Flexible queue formation through obstacles
TABLE 2: Calculated σof UAVs before and after coming
into formation
UAV No. Standard Deviation Standard Deviation
before formation after formation
(σ1) (σ2)
UAV 2 10.5430785734 7.0531634715
UAV 3 5.0412687286 3.1362290768
UAV 4 11.1664821141 3.128475562
UAV 5 36.9613886179 3.5387336333
avoiding considerable fluctuations in either parameter, please
see Figures 9(a) and 9(b) respectively. This validates our
claim that the proposed algorithm reliably maintains tracking
and keeps safe distance between each leader and its follower
in the swarm. The occurrence of momentary peaks in velocity
of some drones happens due to the collision avoidance scene
illustrated in Figure 7.
The relative distances amongst all UAVs are shown in
Figure 10. This is a metric to show how well the formation is
being kept. As the graph shows, the UAVs are spawned from
random locations, then the formation algorithm is initiated
resulting in UAVs moving closer to their respective leaders
while maintaining the minimum required distance. Table 2
shows the standard deviation calculated before and after the
UAVs have reached queue formation. Here, σ1, denotes the
standard deviation of the drones’ distances from the starting
point when the nodes are at random coordinates and until
they come into formation. Whereas, the standard deviation of
the distances calculated from the point the drones reach the
formation until they arrive in the final destination is denoted
by σ2. It is evident from the values shown in the table that the
(a) Leader moves past the obstacle before its
follower reaches it
(b) Follower start navigating towards the destina-
tion and comes into ordered formation when the
leader comes in its range
FIGURE 8: Leader moves past the obstacle before formation
050 100 150
0
50
100
150
Time (s)
Distance (m)
distance 21 distance 43
distance 32 distance 54
(a) Distance of each drone from its respective leader
0
50
100
150
0
2
4
6
8
10
Time (s)
Velocity (m/s)
drone1 drone2 drone3
drone4 drone5
(b) Velocities of all UAVs
FIGURE 9: Distance and Velocity graph of the UAVs
050 100 150
0
50
100
150
200
Time (s)
Relative distances (m)
distance 21 distance 23
distance 24 distance 25
distance 31 distance 34
distance 35 distance 41
distance 45 distance 51
mean
FIGURE 10: Relative distance of all drones from each other
10 VOLUME 4, 2016
Yasin et al.: Energy-efficient Formation Mor phing for Collision Avoidance in a Swarm of Drones
proposed algorithm maintains the formation tightly, without
any significant fluctuations in distances, especially after the
UAVs have reached the desired formation.
For comparing our proposed technique with the state-
of-the-art algorithms, we implemented the formation and
collision avoidance algorithm presented in [23] and [27] and
set it side by side with our proposed method. Figures 11, 12,
and 13 show the simulation results for distance maintenance
between the first three nodes. It can be seen that our proposed
algorithm maintains the distances between the drone-pairs
within a tight range as compared with the reference methods
presented in [23], [27].
23 27
FIGURE 11: Comparison of distance maintenance from
UAV2 to UAV1
23 27
FIGURE 12: Comparison of distance maintenance from
UAV3 to UAV1
23 27
FIGURE 13: Comparison of distance maintenance from
UAV3 to UAV2
The reference algorithm [23] takes action when both edges
of an obstacle are visible, whereas the algorithm in [27]
starts taking collective measures as soon as an obstacle comes
within the detection range, and our algorithm is an extended
version of the implementation of [27] and with the help of
Thin-Plate Splines technique it maintains the formation even
more aggressively and reducing the overall energy of the
system. Furthermore, the authors in [23] have not consid-
ered alternative measures for two or more closely placed
obstacles. If two obstacles are in close proximity to each
other, the method always considers them a single object, even
in the case where a clear gap exists between the obstacles.
This leads to sub-optimal flight paths. Since collision range
is around the obstacles, so the UAVs can go through the
obstacles rather than going around them. In our algorithm, on
the other hand, the detected gaps are taken into consideration.
The algorithm determines if there is sufficient space between
the obstacles for the UAV to go through and takes action
accordingly.
The change in temperature, i.e., the instantaneous value of
the TPS energy function ETPS, and the sum of this parameter
that represents total disturbance suffered by the system of
five drones during the complete flight from the launch of
individual drones to their arrival at the destination of our
proposed approach and the compared works are shown in
Figures 14 and 15.
30
FIGURE 14: Change in Temperature of the system as a whole
150
200
250 237.49
198.1
134.86
Energy
[23] [27] EFMCA
FIGURE 15: Total Energy of the system
There are a few interesting things to note from Figure 14.
Firstly, the initial few seconds show almost zero temperature
for [23], the reason being that this algorithm assumes that
drones are launched in proper formation. The other two
algorithms show a large variation in temperature owing to
the fact that drones are assumed to have been launched from
random locations in close proximity. Here, EFMCA shows
better management of formation as is evident from reduced
overshoots of temperature. The peaks around 40 seconds on
the timeline represent gradual deviation in route to avoid
Obstacle A with minimum disturbance in formation. Finally,
the comparison of widths of peaks around 140 seconds shows
that EFMCA resumes the formation considerably quickly as
compared with the algorithm in [27]. This is a direct con-
sequence of our approach of integrating TPS with formation
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Yasin et al.: Energy-efficient Formation Mor phing for Collision Avoidance in a Swarm of Drones
(a) (b) (c) (d)
FIGURE 16: Simulation snapshots in SwarmLab. (a) 3D view. (b) at the start of simulation. (c) halfway through the simulation,
navigation through the obstacles. (d) towards end of simulation.
and collision avoidance algorithm that brings the drones back
in formation in a timely manner after disturbances caused
by the obstacles. It is to be noted that algorithm in [23]
does not try to bring the drones back into formation after
splitting, as is evident from Figure 14 where the disturbance
as measured by temperature does not return to zero. Thus,
our method is more aggressive in balancing and bringing the
system back to its stable state after disturbances caused by
any obstacles. Also, as explained earlier we employ a non-
rigid mapping function for point set registration of individual
drones to formation locations. Therefore, in case a drone goes
ahead of its leader during a maneuver, rather than slowing
down to retain its original formation position as required by
earlier approaches, we make this drone the new leader. Con-
sequently, the speed of the formation as a whole increases,
resulting in faster completion of the mission. This effect may
be seen by EFMCA peaks occurring gradually earlier than
the peaks of [27] in Figure 14. In order to show the overall
efficiency of our scheme vis-a-vis the competing algorithms,
we calculated the sum of all disturbances suffered by the
system of drones during the complete mission. The result is
shown in Fig. 15 where energy of the system for each of the
three schemes refers to the area under the respective curve
in Figure 14. It is evident from Fig. 15 that a swarm under
our proposed EFMCA algorithm suffers much less overall
disturbance as compared with other known schemes.
A. VALIDATION OF OUR SIMULATION RESULTS
VIS-A-VIS INDUSTRY STANDARD
In order to validate our results further, we chose to de-
ploy our proposed algorithm on SwarmLab: a MATLAB
Drone Swarm Simulator [44], which is an open-source
environment developed by Laboratory of Intelligent Systems
(LIS), Ecole Polytechnique Federale de Lausanne, Switzer-
land. This simulation environment reflects the behaviour of
the industrial drones, and also with the least amount of
redundancy. Furthermore, the physical constraints (e.g. mass,
inertia) are also supported and modelled in this environment.
Figure 16 shows the snapshots of the simulation output,
taken at different intervals by implementing the EFMCA
algorithm in the SwarmLab for observing the behaviour
and effectiveness of the proposed algorithm in a different
environment. Figures 16(a) and 16(b) show the initial place-
ments of the nodes in the 3D and 2D views, with cylin-
drical obstacles placed in the environment. The nodes then
accelerate and decelerate to reach their desired positions
w.r.t. their immediate leaders, as visible from the average
velocity graph in Figure 18(b). Figure 16(c) shows the state
of the swarm navigating through the obstacles at the half-
way stage of the simulation. It is observed that the nodes
maintain the flexible queue formation and rapidly decrease
any disturbances caused due to the presence of the obstacles
in the path. Figure 16(d) shows the snapshot towards the end
of the simulation, where the swarm has successfully managed
to avoid multiple obstacles in its path while maintaining the
defined safe distance from the obstacles.
(a)
(b)
FIGURE 17: Average, minimum, and maximum distance
maintained between the nodes. a) In our environment, b)
implementation in SwarmLab
Figure 17 shows the comparison of the distance main-
12 VOLUME 4, 2016
Yasin et al.: Energy-efficient Formation Mor phing for Collision Avoidance in a Swarm of Drones
tained between the nodes utilizing the EFMCA algorithm
in our own environment and in SwarmLab. The analysis of
the behaviour of the distance maintained by the nodes shows
similar trends in the results obtained from the two environ-
ments. The difference in momentary peaks or disturbances in
Figure 17(a), as compared with Figure 17(b), is due to the ab-
sence of some dynamics, such as a drone’s mass and inertial
movement, in our Python based environment which is still
being developed constantly. However, the average distance
trend comparison between the two environments provide
enough evidence that the algorithm performed as expected
in the state-of-the-art third party simulation environment.
Figures 18(a) and 18(b) show the overall trend of the
velocity of the swarm throughout the simulation, with av-
erage, average + standard deviation, and average - standard
deviation. The initial peaks in the graphs are due to the
nodes accelerating to reach their desired coordinates in the
formation. Moreover, the average velocity trend in Figure
18(b) showcases the smooth acceleration and deceleration,
whereas the sharp momentary peaks Figure 18(a) are due to
the absence of some of the dynamics in our environment.
However, the average trend is similar as in the absence of the
obstacles, the average velocity of the swarm is maintained at
around 3.5 m/s.
0
2
4
6
8
10
050 100
Velocity (m/s)
avg
avg+sd
avg-sd
(a)
(b)
FIGURE 18: Average velocity, average + standard deviation,
and average - standard deviation of the swarm. a) our envi-
ronment, b) SwarmLab
VII. CONCLUSION
In this paper, we proposed a Thin-Plate Spline inspired for-
mation maintenance algorithm for multiple UAVs, integrated
with a collision avoidance capability. We theoretically inves-
tigated the behaviour of the proposed algorithm and tested
it in a simulation environment. The simulations demon-
strated, that the simulated UAVs were able to dynamically
and reliably bypass obstacles without colliding with them
while maintaining the given swarm formation very closely
during maneuvers and reverting to it in a timely manner.
By the ability to accelerate and decelerate on demand, the
drones can efficiently reach their respective leaders or find
their places in the formation when they start at random
coordinates or wander off due to the presence of obstacles
in their vicinity. Furthermore, the decentralized distribution
of the algorithm allows the UAVs to take local decisions
when in close proximity to obstacles, making the method
highly robust and efficient. The collision avoidance scheme
is able to flexibly handle situations with multiple detected
obstacles. Moreover, the algorithm also takes care of the
case where a UAV goes outside the visibility range of its
leader; such lost UAVs are routed towards the destination
by making a temporary formation if necessary. The multi-
priority strategy works appropriately, changing the priorities
of the different parts/functions of the algorithm whenever
needed. As a comparison, we showed that the proposed
algorithm outperforms the two known existing methods [23],
[27], in terms of the response time, flexibility, and robustness.
Another important contribution of our approach is that by
employing non-rigid mapping between drones and formation
positions, the overall speed of the swarm suffers minimum
lag owing to avoidance maneuvers, as compared with the
above referred earlier approaches. This effect can be quite
significant for those missions where the time to reach the
destination is of critical importance.
In our future work, we plan to extend the algorithm to
handle the 3-dimensional movement along with the intro-
duction of other environmental effects such as air drag on
the individual nodes as well as on the overall shape of the
swarm. For instance, in a queue formation, the preceding
nodes will experience a lesser effect of drag and will subse-
quently consume lesser power as compared with the leader.
Similarly, studying the effect of air drag on a multi-layered
V-shaped formation will be interesting to analyse as well.
This study can help in optimizing the resource management
in the swarm. Furthermore, we plan on testing the proposed
approach in real-time by performing practical experiments
and analyzing its effectiveness.
ACKNOWLEDGEMENT
This work has been supported by the Academy of Finland-
funded research project 314048.
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14 VOLUME 4, 2016
Yasin et al.: Energy-efficient Formation Mor phing for Collision Avoidance in a Swarm of Drones
JAWAD YASIN received the B.S. degree in Elec-
trical Engineering from COMSATS University,
Islamabad, Pakistan. M.S. degree in Embedded
Computing from Åbo Akademi University, Turku,
Finland, in 2017 and currently pursuing PhD de-
gree in Embedded and Electronics Engineering
from University of Turku, Turku, Finland.
In 2009, he worked as Teaching Assistant for
one semester in Electrical Engineering Depart-
ment in COMSATS University, Pakistan. From
2009 to 2010, he worked as a Lab and Network Engineer National University
of Computer Emerging Sciences, Pakistan. From 2011 to 2016, he worked
as Hardware Engineer in Nordic IT Oy, Finland. In 2018, he worked as
Teaching Assistant for Advanced Sensors Networking in Department of
Future Technologies, University of Turku, Finland. His research interests
include agent based modeling, swarm intelligence, embedded systems, col-
lision avoidance, and autonomous vehicles.
SHERIF A.S. MOHAMED received the BA de-
gree in Electrical, Electronics and Communication
Engineering from Ain Shams University, Egypt, in
2011. He received an MS degree in Electronics
and Information Engineering from Kunsan Na-
tional University, South Korea, in 2016. He is cur-
rently a Ph.D. student in the University of Turku,
Finland. His research interests include vision-
based navigation algorithms for autonomous ve-
hicles, embedded systems, swam intelligence and
machine learning.
MOHAMMAD/HASHEM HAGHBAYAN re-
ceived the BA degree in computer engineering
from Ferdowsi University of Mashhad, the MS
degree in computer architecture from University
of Tehran, Iran, and PhD with honour from Uni-
versity of Turku, Finland.
Since 2018 he is Post-Doc and lecturer in Uni-
versity of Turku, Finland. His research interests
include high-performance energy efficient archi-
tectures for autonomous systems and artificial
intelligence. He has several years of experience working in industry and
designing IP cores as well as developing research tools.
JUKKA HEIKKONEN has been a professor of
computer science of University of Turku, Finland,
since 2009. His current research as the head of the
Algorithms and Computational Intelligent (ACI)
research group is related to data analytics, machine
learning and autonomous systems. He has worked
at top level research laboratories and Center of
Excellences in Finland and international organiza-
tions (European Commission, Japan) and has led
many international and national research projects.
He has authored more than 150 scientific articles.
HANNU TENHUNEN is chair professor of Elec-
tronic Systems at Royal Institute of Technology
(KTH), Stockholm, Sweden. He has held profes-
sor position as full professor, invited professor
or visiting honorary professor in Finland (TUT,
UTU), Sweden (KTH), USA (Cornel U), France
(INPG), China (Fudan and Beijing Jiatong Uni-
versities), and Hong Kong (Chinese University
of Hong Kong), and has an honorary doctorate
from Tallinn Technical University. He has served
in Technical Program Committee’s of all major conferences in his area, has
been general chairman or vice-chairman or member of Steering Committee
of multiple conferences in his core competence areas. He has been one
of the founding editorial board members of 3 scientific journal, have been
quest editor for multiple special issues of scientific journals or books, and
have contributed numerous invited papers to journals. He has contributed to
over 850 international publications with H-index 41. He have 9 international
patents granted in multiple countries. He is a member of the Academy of
Engineering Science of Finland.
MUHAMMAD MEHBOOB YASIN has been a
Professor (full) of Computer Networks, College of
Computer Sciences & Information Technology, in
King Faisal University, Saudi Arabia since 2011.
He received the B.Sc. degree from University
of Punjab, Lahore, Pakistan in 1975 and M.Sc.
in Computer Science from University of Wales,
Aberystwyth, UK in 1983. He received his PhD
from The Open University, Milton Keynes, UK in
1986. He served in various research and develop-
ment roles in Pakistan Atomic Energy Commission for over two decades
and then moved to academia, serving as Professor, Department Chair and
Dean at renowned institutions in Pakistan. In 2009, he joined the prestigious
Computer Laboratory at Cambridge University, UK as a visiting Professor.
His research interests include computer networks, applied cryptography,
internet of things and cybersecurity.
JUHA PLOSILA (M’06) is a Professor (full) in
Autonomous Systems and Robotics at the Univer-
sity of Turku (UTU), Department of Future Tech-
nologies, Finland. He received a PhD degree in
Electronics and Communication Technology from
UTU in 1999. He is the head of the EIT Digital
Master Programme in Embedded Systems at the
EIT Digital Master School (European Institute of
Innovation and Technology) and represents UTU
in the Node Strategy Committee of the EIT Digital
Helsinki/Finland node. He has a strong research background in adaptive
multi-processing systems and platforms and their design. This includes,
e.g., specification, development and verification of self-aware multi-agent
monitoring and control architectures for massively parallel systems, ma-
chine learning and evolutionary computing based approaches, as well as
application of heterogeneous energy efficient architectures to new com-
putational challenges in the cyber-physical systems and internet-of-things
domains, with a recent focus on fog/edge computing (edge intelligence) and
autonomous multi-drone systems.
VOLUME 4, 2016 15
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... As in (Yasin et al., 2020), the authors in (Wadood et al., 2024) proposes a different solution for formation control of swarm of UAVs on mountainous terrain, but using an different approach. Traditional PSO proved to be an efficient method for path finding problems applied on positioning robots or drones. ...
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