=Paper=
{{Paper
|id=Vol-3074/paper21
|storemode=property
|title=Characterizing the flying behaviour of bird flocks with fuzzy reasoning
|pdfUrl=https://ceur-ws.org/Vol-3074/paper21.pdf
|volume=Vol-3074
|authors=Elisa Perinot, Johannes Fritz, Leonida Fusani, Bernhard Voelkl,Marco S. Nobile
|dblpUrl=https://dblp.org/rec/conf/wilf/PerinotFFVN21
}}
==Characterizing the flying behaviour of bird flocks with fuzzy reasoning==
https://ceur-ws.org/Vol-3074/paper21.pdf
Characterizing the flying behaviour of bird flocks
with fuzzy reasoning
Elisa Perinota,b , Johannes Fritza,c , Leonida Fusanib,c , Bernhard Voelkla,d and
Marco S. Nobilee,f,g
a
Waldrappteam Conservation and Research, 6162 Mutters, Austria
b
Konrad Lorenz Institute of Ethology, University of Veterinary Medicine, Vienna, Austria
c
Department of Behavioural and Cognitive Biology, University of Vienna, Vienna, Austria
d
Animal Welfare Division, University of Bern, Switzerland
e
Industrial Engineering & Innovation Sciences, Eindhoven University of Technology, The Netherlands
f
Eindhoven Artificial Intelligence Systems Institute, Eindhoven University of Technology, PO Box 513,
Eindhoven 5600 MB, the Netherlands
g
Department of Environmental Sciences, Informatics and Statistics, Ca’ Foscari University of Venice,
Venice, Italy
Abstract
The study of the collective behaviour of animals, driving emergent phenomena like bird flocks
flying in formation, is a challenging task. In this work, we present a novel methodology for
the investigation of birds’ behaviour assisted by fuzzy reasoning. Specifically, we collected all
available domain information about in-wake formation flying and used that knowledge to build
a fuzzy inference system able to accurately determine which bird is providing up-wash to a
follower. As proof-of-concept, we tested our approach to the migration data collected during
2019’s autumn migration of Northern bald ibis.
Keywords
fuzzy modelling, Takagi-Sugeno inference, Geronticus eremita, flock behaviour, formation flight
1. Introduction
Among all animal behaviours, collective motion is one of the most challenging to study
yet it has continuously drawn the attention of scientists, not only in biology but also
in computer science. Collective movement refers to a phenomenon in which single
individuals engage in complex and coordinated movements in space and time, which
create characteristic emerging patterns such as swimming fish schools, migrating herds
of herbivores or flying bird flocks [1]. When considering the flocking behaviour, it is
possible to differentiate between birds flying in “cluster formations” – three-dimensional
WILF 2021 – The 13th International Workshop on Fuzzy Logic and Applications, December 20–22, 2021,
Vietri sul Mare, Salerno, Italy
" elisa.perinot@vetmeduni.ac.at (E. Perinot); marco.nobile@unive.it (M. S. Nobile)
~ http://msnobile.it (M. S. Nobile)
0000-0003-0379-8508 (E. Perinot); 0000-0003-4691-2892 (J. Fritz); 0000-0001-8900-796X (L. Fusani);
0000-0001-5454-2508 (B. Voelkl); 0000-0002-7692-7203 (M. S. Nobile)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution
4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
groups of (usually) smaller birds such as starlings [2] or pigeons [3] – and birds flying
in “line formations”, e.g. Canada geese [4] or pelicans [5]. When investigating “cluster
formations”, scientists’ interest is generally focused on how birds turn, take off and land
all at once with an extraordinary synchrony. However, in “line formation”, the focus is
mainly on the aerodynamic advantage experienced by the birds [6, 7, 8]. When a bird
flies, it produces an up-wash (uplifting air vortex) with the outer part of its wings, which
can be exploited by a following individual to save energy during flight. However, the
follower has to maintain a specific position, that is laterally offset respect to the main
direction of the leader, possibly with one of the wingtips overlapping with the leader’s
wingtip. In addition, the follower should never fly right behind the leader as between
the two up-wash regions (one for each wingtip) there is an area of downwash (for more
details, please see [6]). If the bird is flying in this specific position it is said to be in-wake.
The foundation of flocking behaviour – which inspired countless computational intelli-
gence meta-heuristics – lies in the self-organization of each single individual within the
group. Therefore, in both formation types, to better understand how group dynamics
work, it is necessary to unveil the local inter-individual interactions among the members
of the flock [1, 2]. A common approach to unravel intra-flock interactions and social
relationships is to select one bird, determine its nearest neighbour (with respect to a
Euclidean distance) and assume that the latter is providing up-wash to the follower
[3, 9, 10]. However, this might be not the best approach to study line formations as
the frontal nearest neighbour of an individual might not be necessarily the one that is
providing the up-wash. Another approach is based on in-wake areas of fixed size behind
the wing tips of a leading bird [11, 8], though this approach requires educated guesses
for the extent of the up-wash area. To overcome these problems, we propose a new
approach based on the fuzzy logic. Specifically, in this work we define a knowledge-based
fuzzy inference system, based on Takagi-Sugeno reasoning, for the dynamic assessment of
in-wake flying. Our model encompasses all the available information in the literature and
it is here applied to data collected during the migration of a Northern bald ibis flock.
Data collection. The data were collected in the field and from a group of free-flying
Northern bald ibises (Geronticus eremita) during the 2019’s autumn migration in the
frame of an European LIFE+ conservation project (LIFE+12-BIO_AT_000143) led
by Waldrappteam Conservation and Research1 . Every year, a human-raised group of
birds is taught to fly behind a motorized microlight plane with the scope of leading them
in stages along the migration route to the wintering area in Tuscany, where they are
released (see [12] for more details). During the migration in 2019, all the birds in the
flock were equipped with high-precision GNSS loggers, which collected raw-satellite data
from three different satellite constellations, i.e. GPS, Galileo and GLONASS, using a
sampling frequency of 5 Hz. In addition, the ultralight flying with the flock was carrying
a logger. The loggers were attached to the birds using a leg-loop harness and cased in a
3D printed backpack. After every flight, data were downloaded from each logger and the
loggers’ batteries recharged. We tracked the flock flying across six legs of the migratory
1
More information available at: http://waldrapp.eu
flight, but in this study we restricted the analysis to the data collected during the flight
of the 9th of August. During this flight, we acquired the data for 29 birds and for each
of them collected approximately 10500 points during a 35 minutes period. We want
to point out that during these flights the birds follow the microlight but they usually
fly in a separate formation outside of the aerodynamic influences of the aircraft. Only
occasionally, individual birds leave the group and fly directly behind the aircraft [7, 8].
Data processing. After collection, data were post-processed using RTKlib (version
demo5 b33b) [13, 14] and Python (version 3.7.9). The post-processing allows to calculate
the position in the space using a technique called Post Processing Kinematics (PPK).
This methodology – which is different from the simple trilateration and positioning
exploited by common GNSS (most often GPS) receivers – estimates the position with
a cm-level accuracy (1-10 cm ca.), in contrasts with the meter(s) accuracy (1-5 m ca.)
of normal loggers. However, it mandates the support of a stationary base station that
must be located close to the flying path. Specifically, the flight started and ended in
Heiligenberg (Germany) and therefore we relied on the base station PFA300AUT in
Bregenz (Austria). This station belongs to the EUREF Permanent Network [15], which
continuously collect free-accessible high quality GNSS data. Using RTKpost, we first
calculated the positioning of the microlight given the base station and then we used the
microlight as a reference to calculate the positioning of every single bird in the flock.
At the end of this process, we obtained a sequence of snapshots of the flight, composed
of a timestamp and the associated absolute positions of the birds. As a further processing
step, we calculated the pair-wise relative flying direction for combinations of bird dyads
during each snapshot. In order to do so, we performed the following steps:
• for a given snapshot at time 𝑡, we used the positions at time 𝑡 − 2, 𝑡 − 1 and 𝑡 to
calculate the direction of the flight of all birds;
• for each bird 𝐵, we used such directions to calculate its positioning with respect
to every other bird in the flock. Specifically, we roto-translated all coordinates in
order to place 𝐵 in the origin, with a heading aligned to the 𝑦 axis, and calculated
the relative positions of the other birds.
The output of this process is a set of triples denoting the 𝑤𝑒𝑠𝑡|𝑒𝑎𝑠𝑡, 𝑛𝑜𝑟𝑡ℎ|𝑠𝑜𝑢𝑡ℎ, and
𝑢𝑝|𝑑𝑜𝑤𝑛 relative headings of all leader-follower pairs of birds in the flock. We will denote
the components of these vectors as 𝑤|𝑒, 𝑛|𝑠 and 𝑢|𝑑, respectively. For instance, given the
pair of birds 278 (leader) and 279 (follower), 𝑤|𝑒 = 0 m, 𝑛|𝑠 = −1 m and 𝑢|𝑑 = −0.5 m
means that 279 is following 278 by flying with no lateral offset, with a back displacement
of 1m, staying 0.5m lower with respect to the leading bird.
2. Fuzzy modeling and inference
To determine whether an individual in the flock is exploiting the up-wash provided by a
leading bird, a series of circumstances must be verified. Specifically, the circumstances
used to build our model are the following:
• we assume that a bird can exploit only one up-wash at a time;
• we assume a bird can perform in-wake flying by following (i.e., staying behind)
another bird (from now on, “the leader”). Stated otherwise, the component of the
𝑛|𝑠 axis must be negative;
• we assume that in-wake flying can only happen if the following bird is close enough
to the leader (approximately up to 5m), but not too close [7, 16, 17, 18];
• in-wake flying is supposed to be more effective if a bird is aligned with the wing
tips of the leader, and less effective elsewhere. This region represents the optimal
“wingtip overlap” at which birds should be able to better exploit the up-wash
[19, 7, 16, 18, 8, 11], and an ibis has average wingspan of 1.5m;
• in-wake flying is more effective when the two birds are co-planar, i.e., their 𝑢|𝑑
components should be similar [8, 11, 19].
All these assumptions are vague in nature, so that a bird can satisfy one or more
conditions to a certain extent. Fuzzy Inference Systems (FIS) are perfectly suitable to
model this kind of phenomenon. In this work, we exploit a 0-order Takagi-Sugeno FIS,
in which the fuzzified input is the information about the relative spatial relationship
between two birds, while the output is the level of up-wash felt by the following bird.
The assumptions described above led to the definition of the three linguistic variables
in the FIS, namely: “bird_ew”, “bird_ns”, and “bird_plane”, corresponding to lateral
offset with respect to the leading bird (Figure 1a), proximity to the leading bird (Figure
1b), and the co-planarity between the two birds (Figure 1c), respectively.
a) b) c)
Figure 1: Fuzzy sets and linguistic terms exploited by our inwake flying model. Measures on x axis
are in meters. a) lateral offset; b) proximity; c) co-planarity with respect to the leading bird.
The fuzzy sets of the “bird_we” linguistic variable reflect the fact that birds flying
in-wake are aligned with the tip of wing. For this variable, we used two complementary
and symmetric fuzzy sets to denote alignment (“wing-tip-aligned”) and misalignment
(“wing-tip-misaligned”). Off-tip flying reduces the membership to “wing-tip-aligned”,
which drops to zero after 1.8m. The membership drops to zero also behind the leader,
where an area of downwash is expected [20]. It is worth noting that the alignment with
a leading bird (e.g., −0.8 < 𝑤|𝑒 < 0.8) reduces the up-wash and, hence, increases the
membership to “wing-tip-misaligned”. For the linguistic variable “bird_ns” we used
three fuzzy sets to represent three conditions: “close”, “too_close” and “distant”. By
definition, the strength of in-wake rules is zero if the follower is actually in front of
the bird (i.e., when 𝑛|𝑠 is positive); the strength increases when the ibis is behind the
leader, except when it is too close (distance < 0.1m), where the strength goes down
again, because such proximity would imply a collision between the animals. Finally, when
the leading bird is too distant (e.g., when 𝑛|𝑠 < −5m) the membership to the “close”
fuzzy set drops to 0. This is the rationale of the fuzzy sets of the “bird_ns” linguistic
variable. Finally, we assume that plane-aligned ibises are flying in-wake; off-plane flying
reduces the membership to the “same_plane” set (Figure 1c), which ultimately drops to
zero after ±0.75m. This number was taken as it is half a wingspan of the birds. The
assumptions for in-wake flight led to the five fuzzy rules, involving the aforementioned
linguistic variables as antecedents, reported in Table 1. The crisp output values, used
Rule 1: IF bird_ew IS wing_tip_aligned AND bird_ns IS close AND bird_plane IS same_plane
THEN flying IS in_wake
Rule 2: IF bird_ew IS wing_tip_misaligned THEN flying IS not_in_wake
Rule 3: IF bird_ns IS too_close THEN flying IS not_in_wake
Rule 4: IF bird_ns IS distant THEN flying IS not_in_wake
Rule 5: IF bird_plane IS different_plane THEN flying IS not_in_wake
Table 1
Fuzzy rules used by our inwake flying model.
in the consequents, are defined as: in_wake = 1; not_in_wake = 0. Figure 2 shows
three heatmaps that summarize the behavior of the whole FIS: the brighter the color, the
stronger the firing of the “in_wake” rule. The three panels show the area of upwash as
seen from above, (Figure 2a, assuming 𝑢|𝑑 = 0), behind (Figure 2b, assuming 𝑛|𝑠 = 1),
and from the side (Figure 2c, assuming 𝑤|𝑒 = 0). The FIS implicitly defines a region
where the bird feels the up-wash, with the maximum level of in-wake flight being reached
approximately 1m behind one of the tips of the leading bird.
3. Preliminary results
In this section we apply our knowledge-based FIS for the analysis of the time series of
one leg of human-led ibis migration. The FIS was implemented using the Simpful python
library [21] version 2.5.0.
D E F
E L U G B X G
E L U G B X G
E L U G B Q V
E L U G B Z H E L U G B Z H E L U G B Q V
Figure 2: Heatmaps showing the mapping between relative positions and the defuzzified value of the
output: (a) top view; (b) rear view; (c) vertical lateral view.
We run our FIS on the relative position data in each flight snapshot and managed
to reconstruct flock dynamics. An example of the results is show in Figure 3, which
shows the bird flock from above (top left), back (top right), side (bottom left) and using
a perspective view (bottom right). In the figure, each blue dot represents a bird and it is
reported a unique identification number for each individual. If one bird is exploiting the
up-wash of a leader bird, this relationship is denoted by an arrow. The color of the arrow
denotes the strength of the fuzzy rule, ranging from low (blue) to high (red). The FIS is
also able to detect birds that are not flying in the wake: in Figure 3 (bottom right), we
denote such birds using red color, in this case ibises 285, 286, 301 and 309.
Figure 3: Example of in-wake relationships of the flock calculated by our FIS. View of the bird flock
from different perspectives, i.e., above (top left), the back (top right), the side (bottom left) and
perspective view (bottom right). The blue dots represent the positions of birds, while the arrows
denote the in-wake relationship between follower and leader birds. The color of the arrow denotes the
firing strength of the “in-wake” rule, ranging from blue (low strength) to red (high strength). In the
bottom right graph, the red dots represent the birds that are not flying in wake. The green arrows
show the direction towards which the entire flock is flying.
We repeated the analyses for all the snapshots collected during the flight of August
9, 2021. For each bird, we calculated the distribution of its leaders, as determined by
the FIS, during the whole flight. The result of this analysis is shown in Figure 4: each
panel represent the distribution for a specific bird. We use histograms to represent how
278 279 280 281 282 283 284 285 286 287
309 309 309 309 309 309 309 309 309 309
308 308 308 308 308 308 308 308 308 308
307 307 307 307 307 307 307 307 307 307
306 306 306 306 306 306 306 306 306 306
304 304 304 304 304 304 304 304 304 304
303 303 303 303 303 303 303 303 303 303
302 302 302 302 302 302 302 302 302 302
301 301 301 301 301 301 301 301 301 301
300 300 300 300 300 300 300 300 300 300
299 299 299 299 299 299 299 299 299 299
298 298 298 298 298 298 298 298 298 298
297 297 297 297 297 297 297 297 297 297
295 295 295 295 295 295 295 295 295 295
294 294 294 294 294 294 294 294 294 294
293 293 293 293 293 293 293 293 293 293
292 292 292 292 292 292 292 292 292 292
291 291 291 291 291 291 291 291 291 291
289 289 289 289 289 289 289 289 289 289
288 288 288 288 288 288 288 288 288 288
287 287 287 287 287 287 287 287 287 287
286 286 286 286 286 286 286 286 286 286
285 285 285 285 285 285 285 285 285 285
284 284 284 284 284 284 284 284 284 284
283 283 283 283 283 283 283 283 283 283
282 282 282 282 282 282 282 282 282 282
281 281 281 281 281 281 281 281 281 281
280 280 280 280 280 280 280 280 280 280
279 279 279 279 279 279 279 279 279 279
278 278 278 278 278 278 278 278 278 278
0 200 400 600 0 200 400 600 0 200 400 0 250 500 750 0 200 400 0 200 400 600 0 250 500 750 0 200 400 600 0 250 500 750 0 200 400
288 289 291 292 293 294 295 297 298 299
309 309 309 309 309 309 309 309 309 309
308 308 308 308 308 308 308 308 308 308
307 307 307 307 307 307 307 307 307 307
306 306 306 306 306 306 306 306 306 306
304 304 304 304 304 304 304 304 304 304
303 303 303 303 303 303 303 303 303 303
302 302 302 302 302 302 302 302 302 302
301 301 301 301 301 301 301 301 301 301
300 300 300 300 300 300 300 300 300 300
299 299 299 299 299 299 299 299 299 299
298 298 298 298 298 298 298 298 298 298
297 297 297 297 297 297 297 297 297 297
295 295 295 295 295 295 295 295 295 295
294 294 294 294 294 294 294 294 294 294
293 293 293 293 293 293 293 293 293 293
292 292 292 292 292 292 292 292 292 292
291 291 291 291 291 291 291 291 291 291
289 289 289 289 289 289 289 289 289 289
288 288 288 288 288 288 288 288 288 288
287 287 287 287 287 287 287 287 287 287
286 286 286 286 286 286 286 286 286 286
285 285 285 285 285 285 285 285 285 285
284 284 284 284 284 284 284 284 284 284
283 283 283 283 283 283 283 283 283 283
282 282 282 282 282 282 282 282 282 282
281 281 281 281 281 281 281 281 281 281
280 280 280 280 280 280 280 280 280 280
279 279 279 279 279 279 279 279 279 279
278 278 278 278 278 278 278 278 278 278
0 200 400 600 0 200 400 600 0 200 400 600 0 200 400 600 0 200 400 600 0 200 400 0 200 400 600 0 250 500 750 0 200 400 600 0 250 500 750
300 301 302 303 304 306 307 308 309 Not flying inwake
309 309 309 309 309 309 309 309 309 309
308 308 308 308 308 308 308 308 308 308
307 307 307 307 307 307 307 307 307 307
306 306 306 306 306 306 306 306 306 306
304 304 304 304 304 304 304 304 304 304
303 303 303 303 303 303 303 303 303 303
302 302 302 302 302 302 302 302 302 302
301 301 301 301 301 301 301 301 301 301
300 300 300 300 300 300 300 300 300 300
299 299 299 299 299 299 299 299 299 299
298 298 298 298 298 298 298 298 298 298
297 297 297 297 297 297 297 297 297 297
295 295 295 295 295 295 295 295 295 295
294 294 294 294 294 294 294 294 294 294
293 293 293 293 293 293 293 293 293 293
292 292 292 292 292 292 292 292 292 292
291 291 291 291 291 291 291 291 291 291
289 289 289 289 289 289 289 289 289 289
288 288 288 288 288 288 288 288 288 288
287 287 287 287 287 287 287 287 287 287
286 286 286 286 286 286 286 286 286 286
285 285 285 285 285 285 285 285 285 285
284 284 284 284 284 284 284 284 284 284
283 283 283 283 283 283 283 283 283 283
282 282 282 282 282 282 282 282 282 282
281 281 281 281 281 281 281 281 281 281
280 280 280 280 280 280 280 280 280 280
279 279 279 279 279 279 279 279 279 279
278 278 278 278 278 278 278 278 278 278
0 200 400 0 200 400 600 0 200 400 600 0 200 400 0 200 400 0 200 400 600 0 200 400 600 0 200 400 0 200 400 600 0.0 0.2 0.4
Figure 4: 1. Colored bars: distributions of the leader-follower relationships for the 29 birds in the
flock. Each individual is characterized by a unique identification number (top of the graphs and on y
axes). The numbers on the x axis represent the number of snapshots. The star denotes the most
followed bird. 2. Grey bars: proportion of time each bird was flying alone (see text for details).
frequently a bird followed a specific bird, denoted by a unique color. In each panel, the
black star denotes the most frequently leading bird, while the dashed line represents
the theoretical frequency in the case each bird follows any other bird during the flight,
following a uniform probability distribution.
According to our results, many ibises seem to have a preferred bird to follow (e.g., bird
306 mostly followed bird 291 during the flight). Interestingly, the leader bird is often
unique for each bird, with the notable exception of ibis 293 which was the choice of ibises
287, 297, 298, 300 and 307. This result agrees with our observation that 293 was indeed
a dominant male while four out of the five followers were subordinate females (personal
communication). In addition, we extracted the proportion of time that each bird was
flying alone, i.e. was not in the wake of any other individual (Figure 4 graph in grey,
bottom right). Few birds flew more that 40% of the time whether in the front of the
flock or without following any individual (e.g. 283 and 306). That day, both birds were
observed to fly outside the group, near the aircraft, more often than other birds (personal
communication). All the others flew alone between 20% and 40% of the time. Indeed,
birds prefer to fly close together, whether in a three-dimensional flock or in a formation.
4. Future developments
As future development, we plan to extend our approach to develop some ideas and
fix some current issues. First, it is worth noting that, during our data collection, we
also gathered measurements about the energy expenditure of the free-flying birds. Our
hypothesis is that birds can save energy by flying in-wake: if this were the case, this
measure should show some degree of correlation with the firing strengths calculated
by the FIS model. Second, we plan to further investigate the differences between the
results of our FIS-based approach with respect to conventional method based on nearest
neighbour. Preliminary results show that the two methodologies actually yield different
results approximately 60% of the time. Third, we noticed high-frequency changes in the
bird providing the up-wash according to the FIS. Specifically, the model switches between
different individuals in a very short timespan (200/400 ms), which implies the unlikely
circumstance that the following bird is changing for very short time from one to another
leading bird and back. The reason behind this phenomenon is not clear, and we speculate
that it might be due to the parameters used in our membership functions; a data-driven
calibration of the FIS’ fuzzy sets is currently under investigation. One possible option
to mitigate this problem, and reduce the noise fed to the analysis downstream, could
be to smooth out the time series. Finally, it has been suggested that, to save energy,
birds in formation should synchronize their wing flapping cycles with a phase shift
corresponding to the axial distance between leader and follower [22]. When studying line
formation in the Northern bald ibis, Portugal et al. reported that the following birds were,
indeed, flapping in phase with the bird that is providing the up-wash [7]. This ability, to
synchronize wing flapping is possibly a unique feature of specialized formation flyers as
Corcoran and Hendrick could not find such effects in mixed species flocks of shorebirds
[19]. This topic requires, therefore, further in-depth investigation: we will elaborate
this concept by extending the FIS with additional rules taking into consideration when
the two birds are flying in a synchronized fashion. As final future development, we will
relate energy experimental data to positional data to investigate the possibility of using
a data-driven approach (e.g., ANFIS [23], fuzzy relational neural networks [24], pyFUME
[25]) to build predictive models of birds flocking behavior.
Acknowledgments
The project was funded by the Austrian Science Fund FWF (FWF P 30620-BBL). Data
were collected in the frame of a European LIFE+ project, 50 % contribution of the LIFE
financial instrument of the European Union (LIFE+12-BIO_AT_000143, LIFE Northern
Bald Ibis).
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