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Content uploaded by Guido de Croon
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All content in this area was uploaded by Guido de Croon on Oct 04, 2016
Content may be subject to copyright.
On-board Bluetooth-based Relative Localization
for Collision Avoidance in Micro Air Vehicle Swarms
M. Coppola1,†, K.N. McGuire†, K.Y.W. Scheper†, and G.C.H.E. de Croon2,†.
Abstract— A current limitation of using Micro Air Vehicles
(MAVs) in teams is the high risk of collisions between members.
Knowledge of relative location is needed in order to facili-
tate evasive maneuvers. We propose an on-board Bluetooth-
based relative localization method. Bluetooth is a light-weight
and energy efficient communication technology that is readily
available on even the smallest MAV units. In this work, it
is exploited for communication between team members to
exchange on-board states (velocity, height, and orientation),
while the strength of the communication signal is used to infer
relative range. The data is fused on-board by each drone to
obtain a relative estimate of the location and motion of all other
team members. Furthermore, a collision avoidance controller
is proposed based on collision cones. It is designed to deal
with the expected relative localization errors by adapting the
collision cones during flight and enforcing a clock-wise evasion
maneuver. The system was tested with a team of AR-Drones
2.0 flying in a 4m×4m arena at the same height. The system
showed promising results. When using two AR-Drones and off-
board velocity/orientation estimates, the drones were able to fly
around the arena for a cumulative time of 25 minutes with only
one collision. With three AR-Drones under the same conditions,
flight time to collision was 3 minutes. With two AR-Drones
flying with on-board velocity estimation, the time to collision
was approximately 3 minutes due to the disturbances in velocity
estimates. Simulations show that even better results can be
expected with smaller MAVs.
I. INTRODUCTION
Micro Air Vehicle (MAV) applications include
surveillance [1], mapping [2], and inspection of buildings
[3][4] or other infrastructure [5]. State-of-the-art technology
has led to miniaturized MAVs such as the Lisa-S Ladybird
[6] or the Pico-Quadrotor [7]. These platforms benefit from:
lower mass, increased portability, less obtrusive/restricted
navigation in indoor environments, and safer use near
humans. However, these smaller platforms also suffer
from highly limited sensing and computational capabilities.
Allowing several MAVs to operate in a team/swarm
improves their performance by reducing the task execution
time and adding robustness, scalability, and flexibility [8] [9].
Swarm behavior can emerge with fully independent
units that have no awareness of each-other [10]. However,
when a team of MAVs with decentralized control performs
an arbitrary task in a confined indoor space, there is a
non-negligible risk of intra-swarm collisions [11]. This is a
1m.coppola@tudelft.nl
2g.c.h.e.decroon@tudelft.nl
†Micro Air Vehicle Laboratory, Faculty of Aerospace Engineering, Delft
University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
failure condition to be avoided to ensure mission success.
Collision avoidance is facilitated by on-board knowledge
by each MAV of the relative location of close-by team
members. Additionally, knowledge of relative location can
empower more complex team behaviors such as leader-
follower [7] or formation-flying [12].
One method for relative localization is to rely on a
shared reference frame in which each MAV can localize
itself. The MAVs can then communicate, compare their
position coordinates, and infer a relative estimate. In
outdoor tasks, Global Positioning System (GPS) receivers
can be used to obtain global position data that is then
shared [13][14], but this does not function indoors [15].
In order to achieve the same effect without compromising
the aforementioned efforts of MAV miniaturization, several
solutions propose planting external sensors/beacons with
known relative locations, such as: motion tracking cameras
[16], fixed wireless transmitters/receivers [17], or fixed
visual markers [18]. Although effective, these solutions
defeat the purpose of an exploratory task by relying on a
pre-arranged environment. The Simultaneous Localization
and Mapping (SLAM) strategy and its variants attempt to
solve this by generating a common map on-board during
flight [2]. However, when map generation is not part of
the mission, then this is a resource intensive practice to be
discouraged [19], or even beyond the current capabilities of
miniaturized MAVs [6].
The use of direct measurements between MAVs
overcomes these disadvantages. Vision has received
attention, but examples found in literature simplify the
detection task by adopting mounted visual aids in the
form of: colored balls [20], tags [21], or markers [22].
These studies benefit from the combination of relatively
high-resolution cameras, fast processing speeds, and large
markers if compared to more miniaturized drones. However,
test results in the exploratory phases of this study have
led to the conclusion that using vision without such aids
and at lower resolutions (128×96px, as seen on the Lisa-S
Ladybird [23] [24]) becomes highly problematic and prone
to false-positives/false-negatives. Furthermore, performance
is dependent on lighting conditions, which may change.
Other disadvantages of using vision are: the need for
a front-facing camera and flight along its axis, limited
field-of-view, and generally high processing requirements.
Infra-Red (IR) sensors have been proposed as an alternative
but these require multiple units to be arranged in a rigid
arXiv:1609.08811v1 [cs.RO] 28 Sep 2016
structure, leading to a high mass and power consumption
penalty [25].
The work in [26] attempts to overcome the issues
above by using on-board sound-based localization with a
mounted microphone array. The difference between arrival
times at the different receivers is used to infer the relative
bearing. A passive version of this attempted to locate
propeller sounds of nearby MAVs, yet this suffered from
noise coming from the MAV’s own engine. The issue was
overcome by the introduction of a chirp generator to send
audio signals at specific frequencies [27]. Nevertheless, the
method still suffers from noise induced by turbulence, as
well as structural vibrations which compromise the rigidity
of the microphone array [28]. Furthermore, a dedicated
microphone array and chirp generator must be mounted.
For smaller MAVs, this can account for an increase in mass
of 10%-20% [28] [6].
Alternatively, a component that is almost always already
present on all MAVs is a wireless transceiver. This is
generally used for communication with a ground station
[29] [23], but it may also be used for intra-swarm
communication [11]. The signal strength of a wireless
communication decreases with distance from the antenna,
and can be used as a measure for range between MAVs.
This knowledge has already been exploited on-board of
MAVs by attempting collision avoidance using only relative
range sensing [11]. However, range-only relative estimates,
coupled with the significant noise and disturbances, were
insufficient to guarantee safe flight of two or more MAVs
in a confined area.
The contribution in this article is an on-board relative
localization method for MAVs based on intra-swarm
wireless communication. This was implemented using
Bluetooth antennas, which are readily available at a low
mass, power, and cost penalty even on smaller MAVs [23].
In this work, Bluetooth intra-swarm communication is used
as a method for the exchange of own state measurements
and as a measure of relative range (based on the received
signal strength). This allows each MAV to estimate the
relative location of the others. The advantages of this
solution are:a) it provides a relative location estimate at all
relative bearings; b) it has a low dependence on the lighting
and sound conditions of the environment; c) it has low
energy consumption requirements; d) it does not require
the addition of any dedicated sensors. A reactive collision
avoidance strategy tailored to the localization estimates
is also proposed. It is based on the concept of collision
cones [30] [31] but designed to deal with the expected
localization errors.
The remainder of this article is organized as follows. Sec-
tion II introduces the relative localization method. Section III
describes the collision avoidance strategy implemented in
the MAVs. Tests have been performed in simulation and in
the real-world using Bluetooth equipped AR-Drones 2.0 to
determine the performance of the system with respect to col-
lision avoidance. The test environments and methodologies
used are defined in Section IV. All results are described in
Section V and further discussed in Section VI. Section VII
provides concluding remarks.
II. BLUETOOTH-BASED RELATIVE
LOCALIZATION
In this work, collision avoidance is achieved using lateral
evasive maneuvers only. Lateral avoidance is preferred over
height separation in order to limit aerodynamic disturbances
between MAVs [32] [16]. For this reason, there is a need to
determine a full location estimate, the method for which is
explained in this section.
Localization is enabled via direct communication between
the MAVs, which communicate the following on-board
states to each-other: planar velocity in the body frame,
orientation with respect to North, and height from the
ground. With Bluetooth communication, an MAV also
measures the Received Signal Strength Indication (RSSI),
indicating the range between the antennas. Each MAV fuses
the received states, the RSSI, and its own on-board states to
estimate the full relative position of the other MAV. When
multiple MAVs are present, multiple instances of the fusion
filter run in parallel so that each MAV may keep track of
the others.
Section II-A introduces the general localization framework
and relevant variables. Section II-B discusses the relationship
between RSSI and range. Section II-C explains how the
fusion filter is set-up, and Section II-D presents the results
of a preliminary test.
A. Framework Definition for Relative Localization
Consider two MAVs Riand Rjwith right-handed
body-fixed frames FBiand FBj, respectively. See Figure 1
for an illustration.
Fig. 1: Top view of the relative localization framework of
MAV Rjby MAV Ri.xBand yBare the axis of the body
frame FB.zBis positive down-wards (into the page). ψ
denotes the orientation with respect to North. ρji is range
between the origins of FBiand FBj.βji is the horizontal
planar bearing of the origin of FBjwith respect to FBi.
01234
Distance [m]
-80
-70
-60
-50
-40
RSSI [dB]
LD Model
Measured RSSI
(a) RSSI measurements with respect to
distance (green-dotted) and fitted Log-
Distance model (black, solid).
−π−π/2 0 π/2π
Relative Bearing [rad]
-10
-5
0
5
10
Error [dB]
LD model error Lobe
(b) Error of LD model with respect to
relative bearing (green, dotted) fitted with
a second order Fourier series (red, solid).
-15 -10 -5 0 5 10 15
RSSI error [dB]
0
0.02
0.04
0.06
0.08
0.1
0.12
Probability Density [-]
LD Model LD Model with Lobes
(c) Noise about the LD model without
(blue, solid) and with (red, dashed) lobe
impact.
Fig. 2: Results of RSSI measurements during an experiment whereby a Bluetooth-enabled Ladybird MAV was carried in
circles around a fixed Bluetooth antenna. The heading of the Ladybird MAV was kept constant so as to explore the impact
of relative bearing on the model error.
The relative location of Rjwith respect to Rican be
defined as:
~
Pji =xj i yji zji φji θj i ψji.(1)
~
Pji is a vector of the quantities describing the 3-
Dimensional (3D) relative pose of Rjwith respect to Ri. It
is expressed in FBi.xji,yji , and zji are the position of the
origin of Rjin FBi;φji ,θji , and ψji are the roll, pitch,
and yaw angles of FBjwith respect to FBi.
Pitch and roll may be neglected by assuming that quadro-
tors maintain approximately planar orientations with respect
to the ground. ~
Pji may then be re-defined as:
~
Pji =ρj i βji hj i ψji .(2)
Where: ρji represents the range between the origins of
FBiand FBj, see Equation 3; βji is the horizontal planar
bearing of the origin of FBjwith respect to FBi, see
Equation 4; hji is the height of Rjwith respect to Ri;ψji
is the orientation of Rjwith respect to Ri.
ρji =qx2
ji +y2
ji +h2
ji (3)
βji =atan2(yj i, xj i)(4)
B. Signal Strength as a Range Measurement
Let mρji be the RSSI measurement (in dB) correlated
with ρji by a function L(ρj i). The signal strength may be
modeled according to the Log-Distance (LD) model [33]:
mρji =L(ρji ) = Pn−10 ·γl·log10 (ρj i).(5)
In Equation 5: Pnis the signal strength in dB at a nominal
distance of 1 meter, and γlis the space-loss parameter. It
dictates the decay of the signal’s power with distance. For
free-space: γl= 2.0. Experimentally, it has been found that
office buildings can feature 2≤γl≤6[34]. A sensitivity
analysis of the model showed that an accurate identification
of γlhas a low impact on the distance estimate at lower
distances (which is the scope of this article). The LD model
is generally assumed subject to a Zero-Mean Gaussian
Noise (ZMGN) [35] [36].
We analyzed the LD model with a Bluetooth-enabled
Ladybird MAV [6] and a fixed omni-directional Bluetooth
antenna (W1049B by Pulse [37]). The Ladybird MAV was
carried in concentric circles at different distances around
the antenna. Its orientation was kept constant so as to vary
relative bearing throughout the measurements. The results
from a representative data-sample are presented in Figure 2,
to which the LD model is fitted using a non-linear Least
Squares (LS) estimator as in Figure 2a. Among a set of
similar experiments, the standard deviation of the error
about the fitted LD model was found to be between 3dB
and 6dB. This is in line with the findings from [11] and [38].
Figure 2b shows the error of the LD model as a function
of the relative bearing. The presence of antenna lobes is
discerned [11]. This knowledge suggests an extension of the
LD model with an additional gain term that is a function of
relative bearing [11], but this is rejected. Including a term
that is dependent on bearing means that a change in RSSI
can be ambiguously associated to a change in either bearing
or range. Furthermore, the shape of the lobes was found
to be antenna-specific when tested with different MAVs.
Figure 2c shows the error distribution, where a clear skew
is present. A model that includes the lobe from Figure 2b is
seen to reduce the skew. Other disturbances may be caused
by: the interference by the reflection of the signal in the
environment [33] [36], the presence of other signals in the
2.4GHz spectrum [34] [39], or other objects that obstruct
the signal [34].
C. Localization via Fusion of Range and On-board States
Achieving a relative localization estimate requires measur-
ing or inferring the quantities in ~
Pji . Thanks to inter-drone
communication, hji and ψj i are trivially observable by an
MAV Riby taking the difference between its own on-board
state and the received states from Rj:
hji =hj−hi,(6)
ψji =ψj−ψi.(7)
ψiand ψjare the rotations of FBiand FBjwith respect
to a common reference axis. The common axis, as depicted
in Figure 1, is magnetic North. It is measurable by all
MAVs using a magnetometer [40] [41]. hjand hiare the
height of the origin of FBiand FBjwith respect to a
reference height. It could be measured using a pressure
sensor [42] [43] [44] and/or a downward-facing camera [45]
[46]. Finally, ρji is available thanks to RSSI measurements,
which are correlated with range as elaborated in Section II-B.
When hji ,ψji , and ρji are measured, the relative bearing
βji becomes observable [47] [48]. We use a discrete-time
Extended Kalman Filter (EKF) in order to perform sensor
fusion and observe βji. The EKF is chosen due to its efficient
processing and memory requirements [49]. Let Equation 8
be the state transition model from time step kto k+ 1.
~pji
˙
~pi
˙
~pjRi
ψj
ψi
hj
hi
k+1
=
~pji +˙
~pjRi −˙
~pi∆t
˙
~pi
˙
~pjRi
ψj
ψi
hj
hi
k
+~vk(8)
~pji =xj i yji Tholds Cartesian estimates of bearing
and range. ˙
~pi=˙xi˙yiTis a vector of the velocity of
Riin FBi(see Figure 1). ˙
~pjRi is ˙
~pjrotated from FBjto
FBi.∆tis a discrete time step between updates equal to the
time between kand k+ 1.~vkrepresents the noise in the
process at time step k. This state transition model assumes
that all current velocities and orientations remain constant.
The observation model for the EKF is given by Equation 9.
mρji
˙
~pi
˙
~pj
ψj
ψi
hj
hi
k
=
L(ρji )
˙
~pi
R2D(ψji )·˙
~pjRi
ψj
ψi
hj
hi
k
+~wk(9)
mρji is a measurable quantity that is correlated with
ρji . In this case mρji is the measured RSSI in dB during
communication, which is a function of the range ρji as
given by L(ρji), see Equation 5. R2D (·)is a 2D rotation
matrix that uses the relative heading ψji to rotate the state
estimate ˙
~pjRi from FBito FBj.~wkrepresents the noise in
the measurements at time step k. Note that ρji is expanded
as per Equation 3 so as to observe xji and yji .
In the EKF, the measurement noise matrix Ris a diagonal
matrix with the form shown in Equation 10.
R=
σ2
m
σ2
v·I4×4
σ2
ψ·I2×2
σ2
h·I2×2
.(10)
σmis the expected standard deviation of the noise on
mρji .σvis the expected standard deviation of the noise
on ˙
~piand ˙
~pj.σψis the expected standard deviation of
the magnetic orientation measurements. σhis the expected
standard deviation of the height measurements. In×nis an
n×nidentity matrix such that the same standard deviation
transfers to the relevant variables.
Considering the noise analysis of the LD model discussed
in Section II-B, a foreseen disadvantage of using the EKF is
the assumption of Gaussian noise on the RSSI measure. The
effects are limited by adopting a high standard deviation for
the received RSSI, therefore σmis tuned to 5dB. All other
variables in Rcan be tuned according to the expected noise
in the other measurements.
The process noise matrix Qis the diagonal matrix pre-
sented in Equation 11. It needs to be tuned so as to define
the validity of the expected process [50].
Q=
σ2
Qp·I2×2
σ2
Qv·I4×4
σ2
Qψ·I2×2
σ2
Qh·I2×2
.
(11)
σQpis the standard deviation of the process noise on the
relative position update. σQv,σQψ, and σQhare the process
noises for the expected updates in velocity, orientation, and
height respectively. The tuning is made such that a high-
level of trust is put on the relative position update, whereas
lower trust is put on the update of the other quantities.
This promotes convergence towards a bearing estimate and
helps to discard the high noise and disturbance in the RSSI
measurements. In this paper, the values are tuned to the
following: σQp= 0.1, while σQv=σQψ=σQh= 0.5, for
a 1 to 5 ratio.
It is noted that the scheme proposed in this section suffers
from a degenerate motion known as rotation ambiguity [51].
When the path of Rjperfectly matches the path by Riin
a straight line, range-only measurements remain constant
and are not informative for bearing estimation. If the MAVs
do not fly in formation, the probability of this event is
low [51]. The same ambiguity takes place when both Ri
and Rjare static — motion by at least one MAV is required.
D. Preliminary Relative Localization Results
We performed flights with a Ladybird MAV around
the fixed Bluetooth W1049B antenna in order to obtain
preliminary insights of the performance of the EKF during
flight, useful for designing the collision avoidance strategy
proposed in Section III. An Optitrack motion-capture system
[52] was used to guide the MAV and record ground-truth 3D
position, velocity, and orientation. Bluetooth RSSI data was
recorded from the communication between the Ladybird
MAV and the antenna. All data was recorded together at a
rate of 5Hz; this is a current limitation of the Bluetooth
communication set-up, later discussed in Section IV.
0 50 100 150
Time [s]
0
2
4
ρji [m]
LD (inverted) EKF GT
(a) Estimated range (red, dashed) between
Ladybird MAV and Bluetooth antenna
compared to ground truth (blue, solid)
and estimate from inverting the LD model
(green, dotted).
0 20 40 60 80 100 120 140 160 180
Time [s]
-4
-2
0
2
4
xji [m]
EKF GT
(b) Estimated (red, dashed) relative loca-
tion of the Ladybird MAV along the xB-
axis of the antenna compared to ground
truth (blue, solid).
0 20 40 60 80 100 120 140 160 180
Time [s]
-4
-2
0
2
4
yji [m]
EKF GT
(c) Estimated (red, dashed) relative loca-
tion of the Ladybird MAV along the yB-
axis of the antenna compared to ground
truth (blue, solid).
01234
Distance [m]
-80
-60
-40
RSSI [dB]
LD model Measured RSSI
(d) Measured RSSI (green, dotted) at
different ranges and the LD model used
(black, dashed). The parameters of the LD
model are: Pn=−63 and γl= 2.0.
0 20 40 60 80 100 120 140 160 180
Time [s]
0
1
2
3
|~eji |[m]
(e) Magnitude of pose error over time.
Notice the convergence of the error in the
initial seconds.
0123
ρji [m]
0
1
2
3
|~eji|[m]
Error One-to-One Diagonal
(f) Positive correlation between magni-
tude of pose error and distance below a
diagonal line. The errors seen above the
diagonal line are from the initial seconds
prior to convergence.
Fig. 3: Preliminary localization results based on circular flights of a Bluetooth equipped Lisa-S Ladybird MAV around a fixed
antenna. These results have been averaged over 50 iterations of artificial noise added to the velocity, height, and orientation
measurements.
The data gathered was used to process the EKF off-board.
The recorded velocity and orientation data from Optitrack
was altered with Gaussian noise and used as measurements
for the EKF. This simulated the measurement of these
values using on-board sensors. The standard deviation of
the noise given to velocity measurements is σv= 0.2m/s.
The standard deviation of the noise given to altitude
measurements is σh= 0.2m. The standard deviation of the
noise given to orientation measurements is σψ= 0.2rad.
These values were also included in the measurement noise
matrix R. In the LD model of the EKF: Pn=−63dB and
γl= 2.0, assuming free-space propagation.
Figure 3 shows the results of the relative localization
estimates achieved by the EKF. The antenna is Riand it is
trying to localize the MAV Rj. The top row shows the output
of the EKF against Ground-Truth (GT) data. An immediate
benefit observed is the significant reduction in error for the
observed range, see Figure 3a. Estimates for xji and yji are
shown in Figure 3b and Figure 3c. Let ~eji be the error in pose
between the estimated position of Rjand the real position
of Rjwith respect to FBi(for a visual representation,
see Figure 4). |~eji |, the magnitude of ~eji , is shown over
time in Figure 3e. Of particular interest for the subsequent
development of a collision avoidance strategy is the observed
increase of this error with the distance, as seen in Figure 3f.
The increase is explained by the logarithmic relationship
between RSSI and distance. The diagonal (one-to-one) line
in Figure 3f indicates a maximum accepted error magnitude.
When |~eji |is above the line, then the error encompasses the
position of Riitself, rendering it insufficient to select an
appropriate maneuver for collision avoidance. In the results,
this is only observed for data over the first few seconds of
flight prior to the convergence of the EKF.
III. COLLISION AVOIDANCE BEHAVIOR
This section describes the devised planar collision avoid-
ance algorithm. It is based on the Collision Cone (CC) frame-
work [53], adjusted to suit the errors and short-comings of
the relative localization algorithm. The general avoidance
scheme is described in Section III-A and Section III-B.
Some remarks regarding its similarities and differences to
other avoidance strategies found in literature are given in
Section III-C.
A. General Avoidance Strategy
A CC is a set of all velocities of an agent that are expected
to lead to a collision with an obstacle [53]. Consider once
more MAVs Riand Rj. We can then define a set CCj i
that includes all velocities of Ri, defined in FBi, which
could lead to a collision with Rj.
Collision cones are so called because they are geometri-
cally cone-shaped. Figure 4 depicts a collision cone CCj i . It
is constructed using Equation 12 to Equation 14 as follows.
First, a general cone CCj i is defined as in Equation 12. αis
an angle in radians, and xand yare points on xBiand yBi,
respectively. The cone is characterized by an expansion angle
αCC ji , expressed in radians and subject to 0< αC Cj i < π.
CCj i ={(x, y)∈R2;α∈R;|α| ≤ |αCCj i |
2: tan(α)x=y}
(12)
Then, the cone is rotated so as to be centered around the
estimated bearing to the obstacle Rjas in Equation 13,
where: ¯
βji is the estimated βj i,←is an update operator,
and R(·)is a rotation operator for the set.
CC j i ←R(¯
βji )·CCji (13)
Finally, the entire cone is translated by the estimated velocity
of Rjexpressed in FBi, to account for the fact that the
obstacle is moving, as per Equation 14. ˙
~pjRi is the estimated
˙
~pjRi . The operator ⊕denotes the translation of a set by a
vector (for instance, S⊕~s indicates the translation of set S
by vector ~s) [53].
CC j i ←CCji ⊕˙
~pjRi (14)
Estimates of βji and ˙
~pjRi are extracted from the EKF
proposed in Section II. If exact estimates were available,
αCC ji would only be dependent on the radii of the two
MAVs (modeled as circular objects) [30]. Errors may be
accounted for by increasing αCC ji [20]. In the following,
we propose a method to establish the expansion angle
tailored to the errors of the Bluetooth relative localization
scheme.
In Figure 3f it is observed that the magnitude of the
localization error increases with the distance, extrapolated
to the following relationship:
E(|~eji |) = 1
κα
·¯ρji,(15)
where καis a constant coefficient describing the quality of
the estimate. E(·)is the expected value. ¯ρji is the estimated
range between Riand Rj. Note that if κα<1then
Fig. 4: Depiction of CCj i that Riholds with respect to Rj.
The dashed circle is the estimated location of Rj.~ej i is the
localization error. αCCji is the expansion angle of the cone.
E(|~eji |)>¯ρj i, meaning that the potential bearing estimation
error is 2πand it does not provide useful information
for collision avoidance. If κα≥1, then the estimate is
sufficiently accurate to select a collision escape trajectory. In
Figure 3f we observed that errors after the initial convergence
convergence are below the diagonal line of κα= 1. In this
paper, we take this worst-case scenario and select κα= 1.
We then define the expansion angle αCC ji based on the im-
plication of E(|~eji |)on the bearing error with Equation 16:
αCC ji = 2 ·tan−1¯ρji +ri+rj+εα
κα·¯ρji .(16)
riand rjare the radii of the MAVs. In a homogeneous
team: ri=rj.εαis an additional margin, the properties
of which are discussed in Section III-B. αCC ji is subject
to an asymptote on its lower limit as ¯ρji → ∞. Its impact
may be appreciated in Figure 5. The asymptote (denoted
αCC asymptote ) is dependent on the selected value of κα:
αCC asymptote = lim
¯ρji →∞ αC Cj i = 2 ·tan−11
κα.(17)
In this work, καis selected as 1. The asymptote of the
expansion angle is thus π/2.
012345
Distance [m]
0
1
2
3
αCC [rad]
κα= 1 κα= 2 κα= 3 κα= 4
Fig. 5: Effect of καon αCC along distance ρji . The other
parameters are set to ri=rj= 0.1mand εα= 0.5. The
straight lines represent the relevant asymptotes.
In a team of mMAVs, each member Riholds m−1
collision cones that it can superimpose into a single set CC i:
CC i=
m−1
[
j=1
CC j i (18)
If, during flight, ~
˙pi∈CCi, then a clock-wise search about
the zBiaxis (starting with the current direction of flight)
is used to determine the desired velocity for escape from
a collision course. The clock-wise search aims to hold the
nominal desired magnitude for ~
˙pi. If no solution is found,
then the search is repeated for a higher escape speed.
B. Preserving Behavior in Different Room Sizes
Equation 16 does not generalize well to environments of
different sizes when all its parameters (ri,rj,κα,εα) remain
constant. Too small values of καand/or too large values of εα
can enlarge the collision cone too much and restrict freedom
of movement when operating in smaller rooms. This brings
two separate disadvantages, both in part culprits for eventual
collisions:
1) Oscillations/instability in MAV trajectories;
2) Convergence of the EKF suffers due to small noise-like
movements.
Appropriate scaling of the collision cone is achieved by
altering εα, which dictates the slope for the change in αCC
at smaller distances, see Figure 6.
012345
Distance [m]
1.5
2
2.5
3
3.5
αCC [rad]
εα= -0.15
εα= 0.05
εα= 0.25
εα= 0.45
αCCeq
Fig. 6: Effect of εαon αCC along ρji . The other parameters
are set to ri=rj= 0.1mand κα= 0.5.
By re-arranging Equation 16, εαcan be determined with
the following rule:
εα=κα·ρeq ·tan αCC eq
2−(ri+rj)−ρeq,(19)
This equation relies on the pair of parameters ρeq and
αCC eq .αCC eq is the desired angle of expansion at a distance
ρeq. For a given κα,εαcan be adjusted with Equation 19
to adapt the expansion of the cone when ρeq changes. Note
that αCC eq > αCC asymptote . Equation 19 sets the limit
εα≥ −(ri+rj)if κα≥1.
The selection of ρeq and αCC eq is left to the designer
based on the expected circumstances. Due to the conservative
choice of κα, lower values of ρeq would be preferred to
enable mobility. In all tests in this article, ρeq is at a distance
that is half of the expected side length of the (square) arena.
αCC eq is kept at a 1.7rad. In a realistic adaptive task, under
the assumption that the MAVs are equipped with a wall-
sensor, then they could define ρeq on-board based on the
distance to the surrounding walls.
C. Connection with Velocity Obstacle Methods
One may note the resemblance of the proposed avoidance
strategy to the Velocity Obstacle (VO) method. The differ-
ence is that VO selects a new flight direction that minimizes
the required change in velocity [30] [31] as opposed to
the clockwise search suggested here. VO is notoriously
prone to reciprocal dances [54]. These are oscillations in
the trajectory when entities heading towards each-other re-
peatedly select the same escape direction, leading to a left-
right “dance”. Reciprocal dances arise when each entity
(wrongly) assumes that the other will not change its course
and avoidance will not be reciprocal. Several variants attempt
to solve this issue by making the opposite assumption, i.e.
that both entities will try to evade the collision. Examples
include Reciprocal Velocity Obstacle (RVO) [55], Hybrid
Reciprocal Velocity Obstacle (HRVO) [56] [57], and Optimal
Reciprocal Collision Avoidance (ORCA) [58]. In our case,
however, due to the potential for large relative localization
errors, the MAVs are not made to assume that the others
will participate in a suitable and reciprocal escape maneuver.
Reciprocal variants of VO are thus discouraged and reliance
on own estimates and avoidance is preferred. The clockwise
search encourages a preference for right-sided maneuvers
with respect to the current flight direction, automatically
resolving reciprocal dances.
IV. TEST SET-UP
This section describes the tests that have been set up
to establish the performance of the combined system in a
realistic team flight. This has first been done in simulation
in order to establish the limitations, and later in the real-
world, with the different objective of establishing the reality
gap resulting from the use of real RSSI measurements and
real on-board velocity estimates for data exchange between
MAVs.
A. Description of Arbitrary Task for Performance Testing
A controller is designed to instantiate an arbitrary task
and applied homogeneously to all MAVs. The task is
designed such that the MAVs repeatedly seek to pass
through the center of the arena. This is made so as to
provoke several potential collision scenarios and observe
if/how these scenarios are resolved.
Consider a team of mhomogeneous MAVs. Each MAV Ri
is controlled in velocity. Let ˙
~picmd,k be the desired velocity
for Riexpressed in its body-frame FBiat a given time-
step k. Let dwallibe the distance between Riand the arena
border that is closest to it, with dsaf e being a safety distance
to the arena’s borders. Remember that each robot Rifeatures
m−1EKF instances to keep track of the other members and
uses their outputs to determine its collision cone set CCi,
see Equation 18. At each-time step k, the EKF outputs are
updated and CCiis re-calculated. ˙
~picmd,k is then chosen as
follows: ˙
~picmd,k =˙
~picmd,k−1unless conditions M1 and M2
take place.
M1: dwalli< dsaf e and ˙
dwalli<0. This means that Ri
is close to the arena border and approaching it. Then,
˙
~picmd,k is rotated towards the center of the arena. See
Figure 7.
M2: ˙
~pi∈CCi. This means that the current velocity of
Ricould lead to a collision with one or more team
members. An escape velocity is sought according to the
strategy proposed in Section III.
Note that M1 supersedes M2 to ensure that the MAVs
remain within the confines of the arena. At all time-steps,
unless other-wise commanded by the collision avoidance
algorithm, |˙
~picmd,k |=vnominal, where vnominal is a fixed
speed magnitude. The MAVs fly at the same height at all
Fig. 7: Depiction of MAV Risubject to condition M1 at
a time step k.Riis closer to the arena border than dsaf e
allows, and moving towards it (see its velocity, ˙
~pi). When
this happens, the commanded velocity ( ˙
~picmd,k ) is oriented
towards the center of the arena.
times.
The controller described above is implemented as a
call-back function upon the reception of new data from
other MAVs. This runs at 5H z due to the limitations of the
real-world implementation (see Section IV-D). Furthermore,
the MAVs always maintain the same heading with respect
to North, purposely taking advantage of the 6-Degrees of
Freedom (DOF) dynamics of quadrotors. In all experiments
vnominal = 0.5m/s. In all simulations dsafe = 0.25m. In
all real-world tests, for conservative/safety reasons, dsafe
was increased to 0.5m.
Section IV-C and Section IV-D describe the
implementation of the above in the simulation environment
and the real-world, respectively. At this early research stage,
it will be noticed that both implementations equally rely
on an external position sensor in order to enforce M1. In
a real-world task, arena borders would be detected using
environment features such as walls (e.g. [59]) and the center
of the arena would represent an attraction way-point.
In all instances, the MAVs begin the task at different cor-
ners of the arena (this is approximate for the real-world tests).
The EKF is initialized such that the initial position estimate
is towards their initial flight direction (i.e. approximately the
center of the arena). All other states are initialized as null.
The covariance matrix of the EKF is initialized as an identity
matrix.
B. Testing Several Density Configurations
The performance of the task described in Section IV-A
is dependent on how crowded/dense the airspace is. This
has been investigated by altering both arena size and
MAV diameter in different configurations. The investigated
configurations and their respective densities are shown in
Table 8. These will be referred to throughout the remainder
of this article by the numbers in the circles.
Airspace density is calculated by modeling each MAV
as a circle in a square arena. Let Dm,c denote the density
0 0.1 0.2 0.3 0.4 0.5 0.6
MAV diameter [m]
1
2
3
4
5
6
Arena side length [m]
11
10
9
8
7
6
5
4
12
3
2
1
D3,1= 2.4%
D3,12 = 2.4%
D3,11 = 3.7%
D3,10 = 6.5%
D3,9= 14.7%
D3,8= 0.8%
D3,7= 1.3%
D3,6= 2.4%
D3,5= 5.3%
D3,4= 0.1%
D3,3= 0.3%
D3,2= 0.6%
D2,1= 1.6%
D2,12 = 1.6%
D2,11 = 2.5%
D2,10 = 4.4%
D2,9= 9.8%
D2,8= 0.6%
D2,7= 0.9%
D2,6= 1.6%
D2,5= 3.5%
D2,4= 0.1%
D2,3= 0.2%
D2,2= 0.4%
Fig. 8: Matrix graph of all configuration pairs of MAV diam-
eter and side length of square arena considered for testing.
The configuration numbers (shown in the white circles) are
referenced throughout the remainder of this article. Dm,c is
the airspace density for configuration cwhen featuring a team
of mMAVs.
for configuration cwith mMAVs. It is calculated as in
Equation 20.
Dm,c =m·πr2
c
s2
c
(20)
rcis the radius of an arbitrary MAV at configuration c
(all MAVs in a configuration are homogeneous). scis the
side length of the squared arena at configuration c. Tests
were performed with two MAVs (m= 2) and three MAVs
(m= 3).
C. Simulation Environment Set-Up
The simulation environment was built using the Robotics
Operating System (ROS) [60]. It adopts the Gazebo physics
engine [61] and the hector-quadrotor [62] simulation which
together provide a validated platform. 1Multiple instances
of a quad-rotor may be launched in a simulation run. The
core functions (i.e. relative localization EKF and collision
avoidance controller) are developed for and within Paparazzi
Unmanned Air Vehicle (UAV) software [63] [64] 2. This
is so as to be readily portable to the real-world set-up
described in Section IV-D. A ROS module (a.k.a. “node”
[60]) for each MAV simulates the presence of a Bluetooth
RSSI sensor and subsequently enforces the controller
1At the time of writing: ROS is freely available at www.ros.org;
Gazebo is freely available at www.gazebosim.org; Hector-quadrotor is
freely available at wiki.ros.org/hector_quadrotor.
2Paparazzi UAV is an open-source UAV/MAV auto-pilot software
available at https://github.com/paparazzi/paparazzi.
−π−π/2 0 π/2π
Relative Bearing [rad]
-5
-2.5
0
2.5
5
∆Antenna Gain [dB]
Log-Dist Model
Lobe Model
(a) Lobes applied to the simulated RSSI
signals on each simulation. The lobes
superimpose as elaborated in [11].
01234
Distance [m]
0
2
4
Error [m]
Error Diagonal
(b) Localization error over simulation
of a concentric circular flight about a
static antenna The higher errors at 1m
are prior to the convergence of the EKF.
(c) Gazebo visualization of a simula-
tion with 3 MAVs.
Fig. 9: Figures relating to the development of the Gazebo/ROS simulation environment.
described in Section IV-A. The module runs at 5Hz to
match the communication speed between MAVs achieved
in the real-world (see Section IV-D).
The RSSI signal was simulated using the LD model
(Pn=−63dB,γl= 2.0) with added Gaussian noise as
well as horizontal lobes as a function of relative bearing.
The standard deviation of the added noise, with the
exception of the results discussed in Section VI-C, is 5dB.
The lobes were arbitrarily modeled using a third order
Fourier series with unitary weights, see Figure 9a. The
other measurements were altered with the same standard
deviations as in the preliminary tests of Section II-D. With
Figure 9b, we see that the achieved performance of the
simulated on-board relative localization scheme features
similar error magnitudes as observed in Figure 3e when a
similar test is repeated in simulation.
Each configuration from Table 8, unless otherwise stated,
has been tested with 100 trials featuring a maximum trial
time of 500sfor two MAVs and three MAVs. The simulations
are interrupted whenever the actual distance between any
two MAVs is smaller than the sum of their radii, indicating
a collision. A screen-shot of a simulation with 3 MAVs is
shown in Figure 9c.
D. Real-World Environment Set-Up
We executed real-world experiments using AR-Drones
2.0 [65] running Paparazzi. The drones all flew at 1.5m
above the ground within a 4m×4marena. Figure 10 shows
a picture of an on-going experiment with 3 drones.
A BLED112 Bluetooth Smart USB Dongle was used
to provide the AR-Drones with Bluetooth 4.0 capabilities
[66]. All computations for relative localization and collision
avoidance are run on-board of the AR-Drones. The LD
model in the EKF filter was given: Pn=−67dB and
γl= 2.0.Pnwas obtained by a brief hand-held calibration
measurement. The choice of γlwas based on the free-space
assumption [34]. Communication between the AR-Drones
was direct via Bluetooth. The data was sent and received
by means of advertising messages scheduled using a
Self-Organized Time Division Multiple Access (STDMA)
Fig. 10: Picture during a real-world experiment with 3 AR-
Drones 2.0 (encircled in white) inside the arena.
algorithm [67]. Under the STDMA algorithm, each MAV’s
Bluetooth antenna alternates between advertising and
listening, achieving data exchange at a rate of 5Hz.
This enabled direct communication circumventing the
Master-Slave paradigm otherwise enforced by the Bluetooth
standard [68].
Two different real-world tests were performed. Test #1
explored the impact of using real RSSI measurements and
communication. Test #2 then explored the effect of using
on-board velocity estimates. The two tests are described in
more detail in the next two paragraphs.
Test #1 (Optitrack-based state estimation): The primary
objective of this test was to establish the performance of
the relative localization and collision avoidance algorithm
when using real RSSI measurements and Bluetooth
communication. On-board state estimation of velocity,
magnetic North orientation, and height was purposely
avoided in order to be able to ensure regulated noise and
isolate the impact of using real Bluetooth RSSI. Optitrack
[52] was used to provide the MAVs with estimates of their
own states via a Wi-Fi link. These were artificially altered
with Gaussian noises σv= 0.2m/s and σψ= 0.2rad upon
being entered into the EKF. Furthermore, Optitrack position
data was used to guide MAVs according to condition
M1 as proposed in Section IV-A. The enforced arena
size in all experiments was 4m×4m. These experiments
are approximately analogous to Configuration 11 from
the simulated tests (AR-Drones 2.0 are slightly larger in
diameter than 0.5m). Experiments were performed with
both two AR-Drones and three AR-Drones.
Test #2 (On-board velocity estimation): These tests
were performed using two AR-Drones. The objective was to
determine the impact of using realistic velocity sensors on
the relative localization performance and its repercussions on
collision avoidance. Instead of relying on Optitrack, the AR-
Drones estimated their own velocity using on-board sensors
and the the Optical Flow module available within Paparazzi
3. The on-board estimates were then directly communicated
between the AR-Drones using Bluetooth. For safety reasons,
and to isolate the impact of the relative localization estimate
on collision avoidance, on-board velocity estimates were only
used as inputs for the EKF relative localization. The velocity
controller of the AR-Drones remained reliant on Optitrack.
This ensured controlled flight within the confines of the
arena. The drones kept a constant heading towards North
and the same height at all times. No noise was artificially
added to the velocity measurements. All other parameters
remained as in Test #1.
V. RESULTS
A. Simulation Results
All configurations presented in Section IV-B have been
tested under the simulation environment described in
Section IV-C. The objective of the simulations is to study
the performance trends under different environments and
the limitations of the system. The parameter used to assess
the performance is the flight-time to collision, which is the
time that the MAVs managed to fly within the arena whilst
avoiding collisions. This is shown for each configuration
in Figure 11. Remember that simulations were stopped
after 500sof flight in the event of no collisions. For all
configurations, flights with three MAVs show a lower
performance with respect to two MAVs. In the simulations,
the introduction of an additional MAV does not affect the
relative localization performance between MAVs. Therefore,
the performance drop is a result of the team dynamics at
play, namely: 1) increased airspace density; 2) decreased
freedom of movement due to superposition of collision
cones. These two factors are analyzed in the remainder of
this section.
When the arena side length remains constant and the
MAV diameter increases, a decrease in mean flight-time is
systematically present. This is observed when comparing
within the configuration triads 4-7-11, 3-6-10, and 2-5-9,
and the pair 8-12. The result is analogous when MAVs of
the same diameter are used in arenas of different sizes,
as may be noticed by observing the configuration quartets
1-2-3-4, 5-6-7-8, and 9-10-11-12. This implies that a lower
density improved the probability of success, but this is
found to not strictly be the case. Figure 12a shows the flight
3See the module computer vision/opticflow for a more in-depth descrip-
tion. It is noted that this module is under active development.
1 2 3 4 5 6 7 8 9 10 11 12
Configuration
0
200
400
600
Mean Flight time [s]
2 MAVs 3 MAVs
Fig. 11: Mean flight-time to collision for all configurations
with active collision avoidance. The maximum simulation
time for each trial was 500sin the event of no collisions.
The mean flight times without collision avoidance, not seen
in this figure, range between 3.9sand 14.3s.
0 5 10 15
Density [%]
0
100
200
300
400
500
Mean Flight Time [s]
2 MAVs
3 MAVs
(a) Mean flight-time with re-
spect to density
0 5 10 15
Density [%]
0
20
40
60
80
100
Area Coverage [%]
2 MAVs 3 MAVs
(b) Mean area-coverage with re-
spect to density
Fig. 12: Flight parameters with respect to airspace density
based on simulation results.
time to collision as a function of the airspace density. A
portion of configurations show low results in spite of the
low airspace density, and are outliers in the negative linear
trend. These correspond to configurations 1, 2, 5, and 9,
which feature smaller arena sizes. The conclusion is that
room size affects performance even when airspace density
remains constant. This is a limitation of the current status of
the system when operating in smaller room sizes. Its causes
are discussed in Section VI-B.
Figure 12b shows the impact of airspace density on area
coverage for all flights with two MAVs and three MAVs.
Area coverage is measured as follows. The arena is divided
in sections. A section is then considered covered if at least
one of the MAVs crosses it during a trial. Area coverage
is the ratio of covered sections to the total number of
sections. The calculation was performed using standardized
sections of 0.20m×0.20m. Two patterns are discerned.
The first is the general trend that a higher airspace density
leads to a lower overall coverage. This is a combined effect
of a) lower flight times, providing less opportunity for
movement, and b) decreased freedom of movement due
to larger portions of the arena being covered by collision
cones. The second pattern is that flights with three MAVs
systematically achieve lower area coverage if compared to
flights with two MAVs at the same density. This is explained
-1.5
0
1.5
N orth[m]→
-1.501.5
←W est[m]
MAV 1 MAV 2
(a) Emergent circular trajectory
with two MAVs.
-1.5
0
1.5
N orth[m]→
-1.501.5
←W est[m]
MAV 1 MAV 2 MAV 3
(b) Emergent circular trajectory
with three MAVs.
Fig. 13: Trajectories from two exemplary simulated flights of
500sextracted from configuration 10 showing the emergent
circular behavior with two MAVs (left) and three MAVs
(right). The starting positions are shown in green (note that
for the flight with three MAVs this was actually at the
corners, but the first few time-steps were not logged). The
final positions are shown in red.
0123456
Distance [m]
0
1
2
3
4
5
6
Error [m]
(a) Localization error magni-
tude for all flights two AR-
Drones in Test #1.
0123456
Distance [m]
0
1
2
3
4
5
6
Error [m]
(b) Localization error magni-
tude for all flights three AR-
Drones in Test #1.
Fig. 14: Overview of magnitude of relative position estimate
error (|~eji |between all MAVs during all flights with two AR-
Drones (left) and three AR-Drones (right). All data shown
here equally relied on off-board self-state estimates (Test #1).
by analyzing the flight trajectories in more detail, which
show an emergent circular behavior. This behavior may be
appreciated in Figure 13, showing two exemplary runs from
a simulation with two (Figure 13a) and three (Figure 13b)
MAVs from configuration 10. When more than one MAV
to avoid is present, the superposition of multiple collision
cones significantly discourages the pursuit of the desired
trajectory. The result is clock-wise motion along the sides
of the arena for all MAVs. Oscillations along the border are
observed as conditions M1 and M2 alternate.
B. Real-World Results with Optitrack-based State Estimation
(Test #1)
Four flights were performed with two AR-Drones in a
4m×4marena. The cumulative flight-time was 25.3min.
In this time, the MAVs only suffered from one collision,
which took place in the second flight after 5.6min. The
other flights lasted 6.1min,7.6min, and 6.0min; they were
ended manually in order to preserve battery health in light
of low battery voltage.
Six flights were performed with three AR-Drones for a
cumulative time of 15.3min. Five out of six flights ended
due to collisions. The flights ending with collisions reached
a mean flight time of 160s(2.7min) before ending with
collisions. The shortest flight was 33s, the longest flight
was 5.2min. The other flights lasted 1.9min,2.6min,
and 3.0min. The flight without a collision was manually
ended after 2.0min due to low battery voltage. Under these
results, a system with three MAVs can expect a collision
once every 184s(≈3min) of flight under the proposed task.
Figure 14 shows the magnitude of the localization error
(|eji |) for all combinations and during all flights together
with two AR-Drones (Figure 14a) and three AR-Drones
(Figure 14b) in Test #1. For all flights with two AR-Drones,
92% of all estimates are below the expected line of κα= 1.
The minimum performance by an MAV over a flight is
84.8%, and the maximum is 97.6%. For all flights with
three AR-Drones, 84% of points are below the expected line.
Figure 15 shows the errors in bearing and range for all
relative estimates during all flights. For flights from Test #1:
the range error is shown in Figure 15a and Figure 15b, and
the bearing error is shown Figure 15d and Figure 15e. The
mean error with two MAVs features a Root Mean Squared
Error (RMSE) of 0.57rad for bearing estimates and 0.86m
for range estimates. With three MAVs, the RMSE rises
to 0.70rad and 1.14mfor bearing and range estimates,
respectively.
Of particular interest is the amount of times that the
bearing error temporarily diverges towards ±π. In spite of
the shorter cumulative flight time, this error case is more
frequent in the flight with three MAVs. The error does not
necessarily lead to collisions in light of the homogeneous
application of the controller to all MAVs and the abstinence
from assuming reciprocity in the collision avoidance.
Nevertheless, it does introduce a temporary uncertainty
in the system that is not accounted for by the collision
avoidance. Furthermore, the convergence rate for bearing
estimates over flights with three AR-Drones is worse than
with two AR-Drones. This may be appreciated in Figure 16,
which shows the first 30sof Figure 15d and Figure 15e
in more detail. Convergence times for flights with three
MAVs reach up to 30sprior to settling (Figure 16b). By
comparison, the convergence in flights with two AR-Drones
only (Figure 16a) is found to be at most within 5−10s.
0 50 100 150 200 250 300 350 400 450
Time [s]
-4
-3
-2
-1
0
1
2
3
4
Range Error [m]
(a) Overview of range estimate error dur-
ing all flights with two AR-Drones with
Optitrack-based state estimation (Test
#1). The RMSE is 0.86m.
0 50 100 150 200 250 300
Time [s]
-4
-3
-2
-1
0
1
2
3
4
Range Error [m]
(b) Overview of range estimate errors dur-
ing all flights with three AR-Drones with
Optitrack-based state estimation (Test
#1). The RMSE is 1.14m.
0 50 100 150 200 250 300 350
Time [s]
-4
-3
-2
-1
0
1
2
3
4
Range Error [m]
(c) Overview of range estimate errors
during all flights with two AR-Drones
with on-board velocity estimation (Test
#2). The RMSE is 1.18m.
0 50 100 150 200 250 300 350 400 450
Time [s]
−π
−π/2
0
π/2
π
Bearing Error [rad]
(d) Overview of bearing estimate er-
rors during all flights with two AR-
Drones with Optitrack-based state estima-
tion (Test #1). The RMSE is 0.57rad.
0 50 100 150 200 250 300
Time [s]
−π
−π/2
0
π/2
π
Bearing Error [rad]
(e) Overview of bearing estimate er-
rors during all flights with three AR-
Drones with Optitrack-based state estima-
tion (Test #1). The RMSE is 0.70rad.
0 50 100 150 200 250 300 350
Time [s]
−π
−π/2
0
π/2
π
Bearing Error [rad]
(f) Overview of bearing estimate errors
during all flights with two AR-Drones
with on-board velocity estimation (Test
#2). The RMSE is 0.77rad.
Fig. 15: Overview of all relative range (top) and relative bearing (bottom) errors. All plots on the left relate to flights with
two AR-Drones with Optitrack-based state estimation (Test #1). All plots in the middle relate to flights with three AR-Drones
with Optitrack-based state estimation (Test #1). All plots on the right relate to flights with two AR-Drones with on-board
velocity estimation (Test #2).
0 5 10 15 20 25 30
Time [s]
−π
−π/2
0
π/2
π
Bearing Error [rad]
(a) Bearing error for all flights
with two AR-Drones in the first
30s.
0 5 10 15 20 25 30
Time [s]
−π
−π/2
0
π/2
π
Bearing Error [rad]
(b) Bearing error for all flights
with three AR-Drones in the
first 30s.
Fig. 16: Comparison of bearing estimate errors between all
performed flights with two AR-Drones (left) and three AR-
Drones (right) in the first 30 seconds of flight. All data shown
here equally relied on off-board self-state estimates.
C. Real-World Results with On-Board Velocity Estimation
(Test #2)
For Test #2, five flights were performed with two
AR-Drones for a cumulative time of 16min. All flights
ended in collisions. The mean time to collision was 192.4s
(3.2min). The longest recorded flight time was 6.0min.
The shortest flight was 2.0min. The other flights were
2.4min,2.4min, and 3.1min. This is a significant drop in
performance if compared to the flights from Test #1 with
two AR-Drones. The reason is in the increased error in
the relative range and bearing estimates when compared to
flights with two MAVs using Optitrack velocity estimates,
0 20 40 60 80 100 120 140
Time [s]
-2
-1
0
1
2
˙xi[m/s]
Ground truth On-board estimate
Fig. 17: Velocity estimation (red, dashed) of an AR-Drone
along the xBaxis against ground truth velocity (blue, solid).
Notice the small spikes between 30sand 40sand the larger
spikes at ≈55sand ≈125s. Furthermore, notice the
occasional over/under estimation in the regions between 70s
to 80sand 100sto 110s.
see Figure 15c and Figure 15f. The RMSE of the relative
range estimates was 1.18m, whereas the RMSE for relative
bearing estimates was 0.77rad.
The loss in relative localization accuracy is attributed to
the disturbances present in the on-board velocity estimates.
Figure 17 shows an exemplary estimate of the velocity along
the xBiaxis by one AR-Drone during a flight. At different
intervals, it may be seen that the velocity was over or
under estimated for an extended period of time. Furthermore,
significant spikes can be seen at ≈55sand ≈125s. These
spikes were manually limited to a maximum magnitude of
2m/s, yet impose significant disturbance in the localization
estimate. Finally, the standard deviation of the error reaches
≈0.4m/s. This was not accounted for in the EKF, which
still assumed 0.2m/s.
VI. DISCUSSION
A. Performance of Relative Localization
The flights with two AR-Drones from Test #1 returned
low relative localization errors and successful collision
avoidance over a prolonged flight time of 25min with
only one collision. However, a noticeable loss in relative
localization performance was measured when introducing
a 3rd MAV. The effects were longer convergence times as
well as higher relative bearing/range errors that negatively
impacted the performance of the collision avoidance system
when compared to the simulation results. The trend is
assumed to get worse with team larger than 3. A similar
decrease in performance was also observed when using
on-board velocity estimates. This was due to a combination
of over-under estimation of velocity or occasional spikes in
the measurements.
The relative localization scheme uses an EKF. This may
be criticized for its reliance on a Gaussian noise driven
model, which fails to provide robustness against un-modeled
disturbances. Other methods such as robust [69] or adaptive
[70] variants of Kalman filters, or Particle Filters (PFs) [36],
could be be better suited to deal with the circumstances.
However, a naive change in filter can bring increased cost
in computational resources without necessarily guaranteeing
a higher quality output. This is because there are a number
of other limitations. One is that the logarithmic decrease in
RSSI makes it intrinsically insufficient to measure changes
in range at larger distances. Another limitation stems from
the proposed process update equation (see Equation 8).
In order to provide a general scheme and abstain from
introducing more complexities in the system, it is based
on the null assumption that all velocities remain constant.
Improvements may come from including more complex
dynamic properties in the process equation, i.e. acceleration
and jerk.
To make the case that a change in filter is not necessarily
to be associated with an improved performance, we compare
the performance of the EKF to that of the Unscented Kalman
Filter (UKF). The UKF is correct to a higher order [71]
and does not need to be influenced by the assumption of
Gaussian noise [72]. Two implementations of the UKF are
used, one with distribution parameter of 2 (denoted UKF2)
and one with a distribution parameter of 0 (denoted UKF0).
UKF2incorporates Gaussian noise, whereas UKF0abstains
from an initial a-priori knowledge [72]. Figure 18 shows
the results for the same preliminary trial run previously
discussed in Section II-D. All filters were applied to the
same realization of artificial noise on the measurements and
featured the same initial conditions. It may be seen that the
performance is comparable. One reason is that the UKF’s
main strength (lack of linearization [73]) is in vain due to
0 50 100 150
Time [s]
0
0.5
1
1.5
2
2.5
Error [m]
EKF UKF0UKF2
Fig. 18: Comparison of localization error (|eji |) with EKF
(red,dashed), Gaussian UKF (purple, dotted), and non-
Gaussian UKF with distribution parameter = 0 (black, dash-
dotted) against ground truth data (blue, solid). The results are
from one realization of artificial noise on the measurements
from the same data-set used in Figure 3.
the low non-linearity of the process/measurement equations
[74]. This may change if the process equation is altered as
previously suggested. Another reason is that there is still a
considerable impact from un-modeled disturbances in the
environment.
Further investigations are encouraged in order to define a
filter that can lower the expected worst-case error. This would
benefit the system as a whole. The collision cone parameter
καcould be reduced without introducing additional risk. This
discussion is continued in Section VI-B.
B. Performance of Collision Avoidance
In simulation, all configurations have also been tested
without active collision avoidance. In this case, the MAVs
are only subject to condition M1. The obtained mean
flight times range between 3.9sand 14.3s. A z-test with
95% confidence level [75] shows a statistically significant
improvement in flight time for all configurations when using
the collision avoidance method.
Figure 12a shows that an increase in airspace density is
directly correlated with a decrease in performance. Smaller
rooms show poorer performance than larger rooms despite
similar density. The parameter εα, as explained in Sec-
tion III-B, implements room scaling within the collision
cones. However, performance cannot reach the same lev-
els unless the other relevant parameters (i.e. call-back rate
(5Hz), vnominal ,dsaf e, sensor noises) are also changed
accordingly. Two reasons for this are:
•The ratio of arena size to vnominal decreases in smaller
rooms. The rate of data exchange is 5Hz, and this limits
the decision rate of the collision avoidance controller.
With other control parameters remaining constant, the
relative distance traveled in smaller rooms is higher than
in larger spaces.
•Maneuver selection. In smaller rooms, M1 has higher
chances of being called due to more frequent proximity
to the arena borders.
Collisions during real-world flights with three MAVs oc-
curred along the edges of the arena. This is also observed
(a) View #1. The blue AR-Drone (bottom
right) moves towards the right. The red
AR-Drone (middle) turns away from the
black MAV and also towards the right.
(b) View #2. The blue AR-Drone is
trapped in the bottom right corner. The
red AR-Drone continues towards the
right.
(c) View #3. The blue and red AR-Drones
are both trapped at the right edge of the
arena and begin alternately invoking M1
and M2 (see Section IV-A). This ends
with a collision.
Fig. 19: Chronological depiction (left to right) of a collision case in a real-world flight with 3 AR-Drones. Large circles
indicate the ground-truth position in the arena. The collision cones of the blue and the red MAVs are shown. The blue and
red diamonds indicate the current estimates by the blue and the red MAV, respectively.
in simulation. For configuration 11, 81% of the collided
simulated flights with three MAVs ended within 0.5mof the
arena borders. By comparison, only 35% of collided flights
with two MAVs ended within this space. An example from
a real-world flight is shown in Figure 19, recounted by the
three events below.
1. One AR-Drone ends up “trapped” along the boundaries
and is reluctant to make movements towards the center
for fear of collisions. In Figure 19a we see that the
bottom right AR-Drone (blue) turns towards the right.
2. Another MAV turns towards the same side. In Fig-
ure 19b, the central AR-Drone (red) avoids the black
AR-Drone (on left) and also goes to the right. Its current
estimate of the other trapped AR-Drone is temporarily
erratic beyond the anticipated bounds.
3. The second AR-Drone also becomes “trapped” along
the border. As in Figure 19c, the two oscillate along
the border until a collision occurs due to proximity.
This collision scenario does not occur with two MAVs
because of the larger freedom of movement and the more
accurate relative location estimate.
The failure mode described above may be tackled in dif-
ferent ways. One option is to increase mobility by increasing
κα, prompting narrower collision cones. The results in this
article are based on a conservative choice (κα= 1) so as to
account for a worst case scenario, but this could be alleviated
in order to resolve these situations. However, if not accompa-
nied by an improvement in the relative localization estimate,
this can increase the risk of collision. Alternatively, the linear
relationship of the error with distance from Equation 15
could be changed into a piece-wise function in order to limit
growth of the collision cone beyond a certain distance. This
would allow for a higher error tolerance but only for objects
beyond a certain estimated range. For example: κα= 1 if
ρji ≤3and κα= 2 if ρji >3. A third option would
be to implement a selective obstacle avoidance method that
prioritizes between obstacles.
C. Impact of Noise on System Performance
The real-world tests with two AR-Drones using off-board
(Test #1) and on-board (Test #2) state estimation have shown
how the performance of the relative localization algorithm is
dependent on high-quality on-board estimates. The perfor-
mance dropped from one collision in a cumulative 25min of
flight to one every ≈3min. To continue the discussion from
the perspective of the RSSI measurements, this section in-
vestigates the extent to which an improvement in RSSI noise
can lead to improved performance. In simulation, two case-
studies are made. In the first case, the simulated RSSI noise
is reduced from 5dB to 3dB; lobes are still simulated. In the
second case, RSSI noise is kept at 5dB but sensor lobes (all
simulated disturbances) are removed. All EKF and collision
avoidance parameters remain unchanged. The configurations
analyzed are those with the lowest performance: 1, 2, 5, 6, 9,
10. The results are shown in Figure 20. It is systematically
observed that removing the antenna lobes improves the
performance. A lower noise also improves results, yet the
impact is (generally) lower than antenna lobes. The lower
error in relative position estimates successfully translates to
a more successful collision avoidance system. This shows
that performance could be improved further if operating in
cleaner environments or if using higher quality sensors.
VII. CONCLUSION
In real world tests using the solution proposed in this
paper, two ARDrones 2.0 flying in in a 4m×4mspace only
collided once over a cumulative flight-time of 25min. With
three ARDrones 2.0, all else being equal, time between
1 2 5 6 9 10
Configuration
0
100
200
300
400
500
Mean Flight Time [s]
5dB, no lobes 3dB Orig.
(a) Improvements in system per-
formance with two MAVs when
noise/disturbances are reduced.
1 2 5 6 9 10
Configuration
0
100
200
300
400
500
Mean Flight Time [s]
5dB, no lobes 3dB Orig.
(b) Improvements in system
performance with three MAVs
when noise/disturbances are re-
duced.
Fig. 20: Improvements in system performance against origi-
nal results (“Orig.”, black, narrowest) when noise is reduced
from 5dB to 3dB (dark gray, mid width) or when lobes are
removed (dark gray, widest). The left figure is for a system
with two MAVs and right figure is for a system with three
MAVs. For configuration properties, refer to Table 8.
collisions was ≈3min. When the AR-Drones were made
to estimate their own velocity on-board using optical
flow, two AR-Drones collided approximately every 3min
as a result of the disturbances in the on-board velocity
estimate. Simulation trials have shown that smaller MAVs in
the same space would generally lead to lower collision rates.
The combined relative localization/collision avoidance
system as presented and tested in this paper can be further
improved in the future. Aside from hardware improvements,
more investigations are advised in order to reliably reduce
the error of the current relative localization filter. If this is
done, it can translate into a higher freedom of movement
for the MAVs without introducing higher risk in the system.
Otherwise, the introduction of an additional strategy to deal
with the avoidance of multiple team members should also
improve performance when flying with 3 or more MAVs.
To conclude, in this work we have shown that it is possible
to use wireless communication as a relative localization
sensor that can be used on-board of MAVs operating in
a team. This enables swarm behavior without the need
of a dedicated sensors. Based on our results, intra-swarm
collisions, a leading failure condition for MAVs flying in a
limited space, can be successfully addressed by this technol-
ogy provided that a collision avoidance system is used that
properly encapsulates the errors involved.
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