More than the sum of its parts: assessing the coherence and
expressivity of a robotic swarm
Florent Levillain, David St-Onge, Elisabetta Zibetti and Giovanni Beltrame
Abstract— The robotics community is considering the use of
large groups of robots, also known as artiﬁcial swarms for
applications in unknown and dynamic environments. In this
context, swarms of robot will need to interact with users to
accomplish their mission. Unfortunately, little is known about
the users’ perception of group behavior and dynamics, as well as
what is the best interaction modality for swarms. In this paper,
we focus on the movement of the swarm as a group to convey
information to a user: we believe that the interpretation of
artiﬁcial states based solely on the motion can lead to promising
natural interaction modalities. We deﬁne the expressivity of a
movement as a metric to understand how natural, readable,
or easily understandable such movement may appear. We
then correlate expressivity with the control parameters for the
distributed behaviour of the swarm. A user study conﬁrms the
relationship between inter-robot distance, temporal and spatial
synchronicity, and the perceived expressivity of the robotic
As robots make their way into our world, the number of
application domains where they are likely to interact and
cooperate with humans multiplies. Each of these domains
constitutes an opportunity to develop a more natural and in-
tuitive relationship, working on the robots capacity to detect
social attitudes and adopt expressive stances. While social
robotics has mostly focused on humanoid and zoomorphic
robots, new forms of robots are entering the scene. Robot
swarms are one of them, composed of large numbers of
robots that can evolve in formation and adapt easily to
multiple environments. The robustness of swarm systems
comes mostly from their distributed and scalable control. For
interaction with humans, what makes swarms special is that
they have no deﬁned physicality: they can adopt emerging
conﬁgurations depending on environmental constraints, inter-
nal policies and commands issued by a user . This absence
of predictable structure, and the necessity for an observer to
consider multiple individuals, make it necessary to develop
new methods of evaluation to qualify the interaction with
Research on the affective reactions to robot swarms has
only started . So far we possess scanty information
about how a swarm’s motion impacts a user’s emotional
response . Speciﬁcally, we do not know how the state
Dr. St-Onge and Dr. Beltrame are with the Department of Computer and
Software Engineering, ´
Ecole Polytechnique de Montr´
Dr. Levillain is with Ensadlab-Reﬂective Interaction. ´
erieure des Arts D´
ecoratifs, 75240 Paris Cedex 05, France. email:
Dr. Zibetti is with the CHART-LUTIN Laboratory, Universit´
e Paris 8,
93526 Saint Denis Cedex 02, France.
attributed to a swarm (e.g. is it considered as a single entity,
an aggregate of autonomous robots, an ephemeral forma-
tion?) affects its perceived psychological traits (nervous, shy,
aggressive, etc.), as well as the expressivity that may be
attributed to its behaviour. Are the reactions to a robot swarm
similar to those we can feel when observing a school of ﬁsh
or a ﬂock of birds? Is a robot swarm able to impress the
sense of a collective movement organized towards a goal?
To what extent an affective relationship can be established
with an ensemble of robots?
This paper preliminarily addresses the fundamental ques-
tions on the cohesion and on the expressivity of a swarm,
and how they are dependent on a deﬁned set of parameters.
In particular we examine how cohesion and expressivity
allow humans to understand the swarm motion dynamics,
and perceive it as a single behavioral entity, as opposed to a
collection of moving objects. These questions are addressed
with a user study on a small swarm of table-top robots. In the
following, we describe related literature, deﬁne expressivity,
detail our distributed control mechanism, and how it is
related to expressivity measurements.
II. RELATED WORK
This paper relates to two bodies of knowledge that are still
somewhat new in robotics: human-swarm interaction and the
use of non-verbal communication from robots. Both have
some key contributions on which we base this work and the
assumptions used in our study.
A. Human-Swarm Interaction
Human-Swarm Interaction (HSI) differs from common
Human-Robot Interaction (HRI) for the large numbers of
units involved and because it heavily relies on inter-robot
communication. The handful of HSI studies currently pub-
lished focus on speciﬁc interface media, and very few
actually study user reaction/perception. In addition, most are
conducted in simulation, suffering from a reality-gap .
Podevijn et al.  successfully showed by experiments that
the number of robots does not inﬂuence the cognitive load
required from a user if the control is performed on the swarm
as a whole.
To convey information about swarm states, a ﬂexible strat-
egy is to use iconic representation that users can recognize
without having to recall them, such as the top LEDs on
each of the robots , or make the robots emit machinic
sounds . Note that the latter uses sounds to help the user
be aware of a malfunction in the swarm, not to share high-
level state information.
For broader use, one needs to deﬁne the information
conveyed by a swarm, a non trivial task that Cappo et al. 
addressed with swarm behaviour descriptors deﬁned as: 1-
action for the global motion of the ﬂeet, 2-goal, i.e. the
destination of the ﬂeet, 3-shape, maintaining a geometry over
the whole motion, 4-heading of the robots, and 5-manner,
i.e. trajectory variations giving various dynamic attributes
to the movement. Over 1000 possible combinations of be-
haviours descriptors were simulated, but no user interaction
study was performed. The shape descriptor is restrictive for
general swarm motion as it removes the possibility of using
distributed path planning algorithms that would not maintain
a shape throughout the complete motion.
Concerning swarm user interfaces, a notable contribution
was the release of the tabletop robots named Zooids .
These robots led to a ﬁrst study of robots group motion
perception (emotional response)  and they were used to
examine the perception of abstract robotic displays , an
interesting approach for ubiquitous robots. The behaviours
implemented in these studies and the robot control are
centralized, which requires all robots to be connected to a
central node and thus decrease the resilience of the group.
B. Nonverbal communication in robots
Despite the differences between HSI and traditional HRI,
many challenges relative to robots social presence are com-
mon to both ﬁelds. As robot swarms are bound to evolve
inside social territories, they need to develop communication
modalities beyond symbols and signs. Nonverbal behaviours,
social attitudes, emotional expressions constitute important
ingredients for a social bond to be established . For
such a connection to be formed and maintained, several
paths have been explored with traditional forms of robotics.
Mimicking the human silhouette and postural structures, a
humanoid robot can express emotional states using a combi-
nation of body posture and facial expressions . Yet more
abstract, high-level motion patterns can contribute to the
emotional expression, without requiring a human appearance,
or even speciﬁc emotions to be expressed. For instance,
the kinematics of movement have been shown to participate
in the emotional appraisal of an action , . Motion
characteristics such as path curvature and acceleration are
correlated with different levels of perceived arousal and
valence , . Yet, one of the HSI current challenges
relating to human-swarm non-verbal communication, is the
state estimation and visualization of swarms . Besides the
aspect of designing appropriate algorithms, a very important
issue is whether humans may be able to understand swarm
motion dynamics  and consequently emotionally react
to it. To consider the swarm’s speciﬁcity with respect to
nonverbal communication, one needs to take into account
the distributed nature of such an entity, and thus develop
the adequate concepts to determine how socially impactful a
swarm can be. This is what we are considering in this paper,
evoking the notion of swarm expressivity.
III. SWARM EXPRESSIVITY
This work uses the level of expressivity of a swarm of
robots as a behavioral metric. To ensure the context of this
study is well understood, we ﬁrst need to deﬁne expressivity
and explain its relationship with robot control.
A. Expressivity and Coherence
A common denominator for the different modalities of
social presence is the notion of expressivity. An expressive
behaviour can be considered one that successfully transmits
a particular emotion, an attitude, or a general disposition
to act and react in certain ways. Phrased by Simmons &
Knight , expressivity represents the ability to “convey
an agent’s attitude towards its task or environment”. The ex-
pressivity of a movement determines how natural, readable,
or easily understandable this movement may appear. Thus,
expressivity determines to a great extent the capability for an
intuitive and transparent interaction with a robot, including
the interaction with a robot swarm.
Because of the distributed nature of robot swarms, the
notion of expressivity is bound to take a different meaning
from traditional approaches that connect expressivity to ges-
tural and morphological properties. A swarm has no body nor
body parts to express feelings or attitudes. Without a deﬁnite
physicality, a swarm can reconﬁgure and adapt to different
environments and commands coming from the user. In this
context, an observer has to consider the emergent properties
resulting from multiple individual behaviours, for instance
the tendency for the individuals to remain close to each
other, or to adopt similar velocities. Determining a swarm’s
expressivity is therefore a different process than considering
the movements of a single robot, or even of a small group of
centralized robots. Instead of relying on body and biological
motion perception, assessing the behaviour of a swarm
depends on speciﬁc computations that rely on ensemble
perception, that is the representation of a collection of objects
as a single entity, and to attach perceived properties, such as
mean orientation or velocity, to this entity .
The literature on swarm behaviour often distinguishes
two different parameters that govern the representation of
a swarm as a coherent entity , : a parameter of
cohesion that represents a tendency for individuals to remain
close to each other, and a parameter of synchronization. The
synchronization can be in terms of velocity or alignment. For
the purpose of this article, we make a distinction between
three parameters (Table I): a parameter of aggregation,
corresponding to the impression for an observer that the
robots forming the swarm tend to stay together rather than
scattering; a parameter of synchronization, or the impression
that the robots are aligning their movements; and a parameter
of leadership addressing the impression that the robots are
following or chasing a member of the swarm. More specif-
ically, we will use the term “cohesion” to refer to a global
property resulting from the sum of the three aforementioned
parameters and to construct a representation of the robot
THE PAR AMET ERS GO VE RN IN G TH E RE PR ES EN TATIO N OF A RO BOT
SWAR M AS A C OH ER EN T EN TI TY.
aggregation the tendency to perceive the robots as re-
maining close to each other
synchronization the tendency to perceive the robots as syn-
chronizing their movements
leadership the tendency to perceive the robots as fol-
lowing one of theirs
B. Swarm bio-inspired control
Many biological societies which consist of relatively sim-
ple members (creatures) can collectively perform complex,
meaningful, and intelligent tasks. Among the most popu-
lar formalization of biological swarm behaviours, potential
functions are a simple, yet ﬂexible control approach. Ar-
tiﬁcial potential functions have been used extensively for
robot navigation and control, for instance in  and .
In Brambilla’s swarm taxonomy , the potential-based
methods are part of the virtual physics-based designs. These
methods assume that the robots are able to perceive and
distinguish neighboring robots and obstacles, and to estimate
their distance and relative position. Each robot then computes
a virtual force vector:
, where θiand diare the direction and the distance of
the ith perceived obstacle or robot and the function fi(di)
is derived from an artiﬁcial potential function. One of the
most commonly used artiﬁcial potentials is the Lennard-
Jones potential, adapted for our physical system as shown
in Fig. 1.
Averaging potential force algorithms such as Lennard-
Jones are referred as the ﬂocking behaviour. The two parts
of the potential equation represent the attractor and repulsor
effect. This potential is driven by two parameters: the target
distance for the system to be stable and the gain of
the potential. While the equation itself requires only basic
arithmetic operations and a few parameters, it is based on
the assumptions that each robot has communication with its
neighbors and their relative position.
Based on its popularity, we selected Lennard-Jones po-
tential, as derived in Fig. 1, to control the behaviour of
our robotic swarm. In this control approach, a goal (target
location) is represented as an attractor inﬂuencing the whole
C. Control attributes
A simple behaviour in mobile swarm systems, such as
ﬂocking, often leads to emergent states . Without formal
analytical model of the robots in their ecosystem, the control
parameters must be optimized from simulations. One can
then observe and deconstruct the transient states generated by
a given simple set of control parameters. In this work, instead
of directly mapping the control parameters to coherence and
0 10 20 30 40 50 60 70 80
Fig. 1. Lennard-Jones potential adapted for wheeled robots formation. The
’-’ and ’+’ domains are respectively the repulsive and attractive parts, for
which the pivot point is set with parameter t.Dis the distance between
two robots and a parameter acting as a control gain on the potential.
expressivity, we designed a set of higher level motion control
1) the average inter-robot distance,
2) the spatial synchronicity of the swarm, i.e. the robots
move as a cohesive group, and
3) the temporal synchronicity of the swarm, i.e. the robots
Each attribute is positioned on a continuous range
(close/far, synchronized/unsynchronized), by the behaviour
control parameters. Indeed, increasing the distance (target)
parameter alone in a Lennard-Jones potential lead to an
unstable and unpredictable inter-robot distance over time.
Therefore, the epsilon/target pair has to be manipulated to-
gether to get a stable formation for each inter-robot distance.
Leveraging the non-stable spectrum of the range of these two
parameters, one can also inﬂuence the spatial synchronicity
of the group. In other words, the more unstable a given pair
of parameters is, the more sparse the robot motion will be.
Temporal synchronicity requires the use of another control
parameter in the potential deﬁnition: the delay or latency for
each robot in registering a goal attractor. By delaying the
inﬂuence of a goal’s attraction on certain robots, we inﬂuence
the temporal synchronicity. For instance, a leader robot can
notice the goal attractor seconds before the rest of the swarm,
thus creating a break in the temporal synchronicity.
The three motion control attributes we just described gave
us the possibility to assess to which extent the expressivity
attributed to the swarm depends on certain emergent states.
Given the necessity to consider multiple individual robots,
we surmise that an observer has to represent the swarm
as a single entity before attributing any kind of properties
to its behaviour. We can suppose therefore that a certain
level of perceived cohesion is necessary for expressivity to
develop, and we should expect to observe a relationship
between the perceived cohesion, as measured by parameters
of aggregation and organization, and a score of expressivity
attributed to the swarm.
We make the following hypothesis:
H1 Considering the swarm as a coherent and stable entity
should depend on the possibility to identify moments
of aggregation and organization in the swarms move-
H2 Expressivity should also be related to the parameters of
aggregation, synchronization and leadership, inasmuch
as a sufﬁcient level of cohesion is necessary for the
swarm to be considered as a single entity. However,
excessive cohesion may be detrimental to the overall
expressivity if it results in stereotyped motion patterns.
IV. USER STUDY
To enhance our knowledge on the relationships between
coherence and expressivity in a robot swarm, we conducted
a user study focused on the validation of the previously
We recruited 27 participants with good knowledge and
experience of dance. For this study on swarm motion per-
ception, we intentionally targeted this speciﬁc background
to give us sensible insights on the slight differences in each
of the swarm motion states. Dancers and choreographers are
THE S IX E XP ER IM EN TAL VARI AB LE S.
S+ robots tend to remain close together
S- robots tend to scatter
T+ robots tend to move simultaneously
T- robots tend to follow a leader
D+ robots are moving with large distances be-
D- robots are moving with small distances be-
the experts of body motion, let it be human or artiﬁcial.
We believe the conclusions obtained from their answers can
better help us deﬁne the motion parameters for a broader
spectrum of users. From the 27 participants, 4 are men, 22
women and 1 selected ’other’; two thirds are dance students
(19), while the others are freelancers (8). The participants
did not receive any kind of ﬁnancial compensation for the
study: they participated out of curiosity for natural interaction
with robotic systems. The study protocol was approved by
the Paris 8 University research board and Polytechnique
eal’s ethical committee. Participants signed an in-
formed consent form to partake in the study.
To illustrate the different motion patterns in multiple
sequential studies, we alternated between two sets of six
Zooids robots. The Zooids are small table-top robots of 2.6
cm diameter, localized from structured light emitted by a
ceiling projector . While our behavioural scripts can be
ported on any hardware platform, we selected the Zooids
for the minimal setup time and ease of transportation. The
Zooids were programmed to obey to pre-calibrated motion
scripts. While the exact path of each robot is not determined,
Fig. 2. Six Zooids moving toward the user to form a ﬁgure. The green
letters show the successive goals covered by each motion sequence.
THR EE S CA LE S TO AS SE SS T H E VALUE S OF C OH ER E NC E AN D
EX PR ES SI VI TY ATT RI BU TE D TO T HE S WARM .
1 on a scale from 0 to 6, indicate to which extent you agree with the
•the robots tend to stay in groups
•the robots tend to synchronize their movements
•the robots tend to follow one of theirs
2 on a scale from 0 to 6, indicate to which extent you agree with the
following statement: the robots form a coherent and stable group
and seem to progress while connected to each other
3 on a scale from 0 to 6, how would you evaluate the expressivity
of the robot swarm?
the group motion parameters and goal locations are scripted.
As shown in Table II, the three high level motion attributes
described earlier where used as binary inputs, generating 8
possible combinations, i.e. 8 different motion scripts. Each
motion followed the same goal sequence (see Fig. 2): (1)
from point A to point B, (2) from point B to point C, (3)
from C to B, (4) from B to C, and (5) from C to A.
Participants were asked to sit in front of the table on which
the Zooids performed. They had a 14 questions to answer on
a tablet (available in French and English) after observing
each sequence. Sequences were shown only once to the
participants, but they were played following one of three
possible orders: 1-2-3-4-5-6-7-8, 5-6-7-8-1-2-3-4 and 1-2-7-
8-3-4-5-6. The motion sequences were triggered one at the
time by the experimenters when the participant conﬁrmed all
questions were answered. The experimenter also explained
beforehand that an unknown number of motion sequences
going through the same goals would be automatically gen-
erated with different motion attributes.
To assess the values of coherence and expressivity at-
tributed to the swarm, participants completed a survey com-
prising three different scales (see table III) : (i) a scale eval-
uating the organization perceived in the swarm’s behaviour;
(ii) a scale measuring the cohesion attributed to the swarm
(i.e. whether it is considered as a coherent and stable entity)
; and (iii) a scale assessing the level of expressivity of the
swarm’s behaviour. For each item of the different scales, we
used a seven-point Likert scale with response ranging from
0 (strongly disagree) to 6 (strongly agree).
Fig. 3. Average scores of expressivity for the different conditions of
spatial synchronicity (S+/S-), temporal synchronicity (T+/T-), and inter-
robot distance (D+/D-).
This study presents a large number of tied ranks for a rel-
atively small dataset (27 participants). We used Kendall’s τb
correlation test to assess the contribution of each parameters
in our dataset. We extract the perceived organization from
the measures of cohesion and expressivity. As we could not
assume that the psychological distance between the scores of
expressivity and between those of cohesion were equivalent,
we used an ordinal logistic regression to examine the effect
of spatial synchronization, temporal synchronization, and
distance on both perceived coherence and expressivity.
How do the parameters of perceived organization con-
tribute to the cohesion attributed to the swarm?
We found a positive correlation between cohesion and
tendency to stay in groups: a higher perceived tendency for
the robots to stay in groups is more likely to be associated
with a higher perceived cohesion (τb=.398,p < .001).
Similarly, we found that a higher perceived tendency for
the robots to synchronize their movements is more likely to
be associated with a higher perceived cohesion (τb=.440,
p<.001). Finally, we found a signiﬁcant positive association
between the perceived tendency for the robots to follow one
of theirs and the cohesion attributed to the swarm (τb=.309,
How do the parameters of perceived organization con-
tribute to the expressivity of the swarm?
The correlation scores were less important than for the
cohesion, but we still found a positive signiﬁcant association
between expressivity and the perceived tendency for the
robots to stay in groups (τb=.148,p=.008), as well as
the perceived tendency for the robots to follow one of theirs
(τb=.197,p<.001). While the tendency to stay in groups
and the possibility to perceive chasing relationships between
the robots seem to beneﬁt the expressivity of the swarm,
an excessive level of synchronization may be detrimental
to this measure, as indicated by the absence of signiﬁcant
Fig. 4. Average scores of cohesion for the different conditions of
spatial synchronicity (S+/S-), temporal synchronicity (T+/T-), and inter-
robot distance (D+/D-).
association between the perceived tendency for the robots to
synchronize their movements and expressivity (τb=.033,
How the synchronization and distance between the robots
affect the expressivity and cohesiveness of the swarm?
Temporal synchronization had a signiﬁcant effect on the
expressivity of the swarm (see Fig. 3). With temporally
asynchronous conditions, expressivity was 1.647 (95% CI,
1.012 to 2.681) times more likely to increase (χ2(1) =
4.028,p=.045). However, we did not ﬁnd an impact of
spatial synchronization: the odds of spatially asynchronous
conditions to be considered expressive was similar to that of
spatially synchronous conditions (odds ratio of 0,698, 95%
CI, 0.430 to 1.134), χ2(1) = 2.107,p=.147. Similarly, the
odds of large spacing conditions to be considered expressive
did not differ from that of small spacing conditions (odds
ratio of 1,389, 95%CI, 0.855 to 2.256), χ2(1) = 1.761,
Compared to expressivity, the cohesion score was affected
principally by spatial synchronization (see Fig. 4): with
spatially asynchronous conditions, cohesion was 0.321 (95%
CI, 0.194 to 0.530) times more likely to decrease (χ2(1) =
19.725,p < .001). Temporal synchronization and distance
did not affect signiﬁcantly the score of cohesion: temporal
synchronization (odds ratio of 0,661, 95% CI, 0.407 to 1.075;
χ2(1) = 2.787,p=.095); distance (odds ratio of 0,859, 95%
CI, 0.530 to 1.392; χ2(1) = 0.381,p=.537).
In this study on the perception of swarm behavior, we
assumed that the expressivity of a swarm is dependent on a
sense of coherence emanating from the robots movements,
itself contingent upon parameters of aggregation, synchro-
nization and leadership. We veriﬁed the hypothesis that the
score of cohesion (measuring to what extent people consider
the swarm as a coherent and stable entity) is linked to
the possibility of identifying moments of aggregation and
organization. We found indeed that all the three parameters
we measured (tendency for the robots to stay in groups, to
synchronize their movements, and to follow one of theirs)
were positively associated with the score of cohesion. As
predicted, the relationship between those parameters and
expressivity is slightly more complicated. Motion patterns
considered expressive are more likely to be associated with
a higher level of aggregation and with the impression that
the robots were following one of them, but we did not
ﬁnd a signiﬁcant correlation with the score of synchro-
nization. We also found that conditions more favorable to
expressivity are those in which movements are temporally
asynchronous, conﬁrming the idea that a high synchronicity
may be detrimental to expressive patterns. It is interesting to
observe that, contrary to the score of expressivity, the score
of cohesion is mainly affected by spatial synchronization,
with spatially asynchronous conditions being considered less
cohesive. We observe an interesting relationship between
the two parameters: we postulate that a sufﬁcient level of
cohesion is necessary for the swarm to be considered expres-
sive (hence the positive correlation between expressivity and
the aggregation and organization parameters), but coherence
and expressivity dissociate with respect to the impact of
temporal synchronization (detrimental to expressivity) and
spatial asynchrony (detrimental to cohesion).
In this work, we presented the preliminary results of a user
study focused on the perception of swarm behaviours. The
expressivity and coherence of the robot group was expressed
in term of high level control attributes, injected as control
parameters of a common distributed behaviour: ﬂocking.
The results show that the perceived cohesion of the group
increases with their tendency to stay in groups (be organized)
and their spatial synchronicity. The expressivity of the swarm
was also increased by their tendency to stay in groups, but
was reduced by the temporal synchronicity. Somehow our
contribution is the prerequisite to further address the question
of the “establishment of a possible affective relationship with
the swarm as a behavioral entity” . We believe these
preliminary results represent a stepping stone on the path to
a better understanding of artiﬁcial swarm perception.
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