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This paper describes ideas and initial experiments in embodied imitation using e-puck robots, developed as part of a project whose aim is to demonstrate the emergence of artificial culture in collective robot systems. Imitated behaviours (memes) will undergo variation because of the noise and heterogeneities of the robots and their sensors. Robots can select which memes to enact, and—because we have a multi-robot collective—memes are able to undergo multiple cycles of imitation, with inherited characteristics. We thus have the three evolutionary operators: variation, selection and inheritance, and—as we describe in this paper—experimental trials show that we are able to demonstrate embodied movement-meme evolution.
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Winfield, A. and Erbas, M. (2011) On embodied memetic evolution
and the emergence of behavioural traditions in robots. Memetic Com-
puting, 3 (4). pp. 261-270. ISSN 1865-9284
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Noname manuscript No.
(will be inserted by the editor)
On Embodied Memetic Evolution and the Emergence of
Behavioural Traditions in Robots
Alan FT Winfield ·Mehmet Dincer Erbas
Received: date / Accepted: date
Abstract This paper describes ideas and initial ex-
periments in embodied imitation using e-puck robots,
developed as part of a pro ject whose aim is to demon-
strate the emergence of artificial culture in collective
robot systems. Imitated behaviours (memes) will un-
dergo variation because of the noise and heterogeneities
of the robots and their sensors. Robots can select which
memes to enact, and – because we have a multi-robot
collective – memes are able to undergo multiple cy-
cles of imitation, with inherited characteristics. We thus
have the three evolutionary operators: variation, selec-
tion and inheritance, and – as we describe in this paper
– experimental trials show that we are able to demon-
strate embodied movement-meme evolution.
Keywords Robot imitation ·Artificial Culture ·
Memetic evolution ·collective robotics
1 Introduction
This paper presents both ideas and initial results from
an ongoing multi-disciplinary research project called
“the emergence of artificial culture in robot societies”
whose overall aim is to investigate the processes and
mechanisms by which proto-cultural behaviours, better
described as traditions, might emerge in a free running
collective robot system. We accept, as a working hy-
pothesis, the idea that mimesis and embodiment are
A Winfield ( ) ·M Erbas
Bristol Robotics Laboratory
University of the West of England, Bristol, UK
Tel.: +44 117 328 2211
E-mail: Alan.Winfield@uwe.ac.uk
M Erbas
E-mail: Mehmet.Erbas@brl.ac.uk
essential pre-requisites for cultural evolution [5]. It fol-
lows that since our aim is to demonstrate artificial cul-
ture we need a system of embodied artificial agents, i.e.
robots, in which robots are able to learn socially from
each other, by imitation. This group of robots, which
we call ‘Copybots’1, require an environment in which
behaviours can be copied, by imitation, from one robot
to another and we refer to this environment as the ‘ar-
tificial culture lab’.
Importantly the Copybots implement a form of em-
bodied imitation in which one robot can copy another’s
behaviours only by observing with its physical senses
and then transforming that sequence of sense-data (per-
ceptions) into motor actions. We do not allow the robots
to transmit behaviours (i.e. sequences of motor actions)
directly from one to another. This means that the Copy-
bots have to overcome essentially the same problems of
inferring each others’ behaviours from possibly unre-
liable first-person perceptions as any embodied agents
(robots, animals or humans), yet at same time the Copy-
bots implement a rather minimal model of social learn-
ing by imitation. We argue that this embodied yet ab-
stract model of social learning, by imitation, provides
both a degree of biological plausibility and opportuni-
ties for unexpected emergence that would not be present
in an agent-based simulation.
Dawkins coined the term ‘meme’ to describe a unit
of cultural transmission [7], and we use this terminol-
ogy here. We propose a definition of a robot meme as
follows: a contiguous sequence or package of behaviours
copied from one robot to another, by imitation. In the
artificial culture lab we ‘seed’ each Copybot with ini-
tial behaviours which, in this paper, are self-contained
movement sequences. We then free-run the Copybots so
1After [5], pages 106-107
2 Alan FT Winfield, Mehmet Dincer Erbas
that robots alternate between enacting movement se-
quences and watching (and learning) those sequences.
The first-generation copy (child) of the initial seed be-
haviour may then itself be copied giving a second gen-
eration copy in a free-running iterative process that
means we have behavioural heredity. The errors that in-
evitably occur in embodied robot–robot imitation, due
to noisy sensors, imperfect observation and the estima-
tion process of inferring motor actions, will give rise
to variation in imitated behaviours. If, furthermore, we
allow robots to select which socially learned behaviour
to enact, then we have the three evolutionary operators
necessary for behavioural (i.e. memetic) evolution. The
artificial culture lab provides us with the infrastruc-
ture and tools needed to track and record these possibly
complex sequences of interactions for later analysis.
We propose a definition for ‘artificial traditions’ as
follows: measurable and sustainable differences in the
memes across different groups of robots, where those
memes can be traced back to common ancestral memes.
We hypothesise that the system outlined in this pa-
per, might provide the conditions in which we could ob-
serve both memetic evolution and the emergence of new
memes which, perhaps because they are suited to the
robot’s physical or sensory morphology, or for entirely
contingent reasons, become dominant in the group of
Copybots, i.e. new artificial traditions.
Before proceeding it is important to clarify the dis-
tinction between the terms memetic evolution, used in
this paper, and memetic algorithm. A memetic algo-
rithm is generally taken to be a population-based ge-
netic algorithm in which some form of individual learn-
ing also takes place; for a review of memetic algorithms
see [15]. In the work of this paper, however, there is
no genetic evolution. Instead discrete behaviours, which
are transmitted by imitation (social learning) are them-
selves subject to variation, selection and inheritance.
Thus we use the term memetic evolution to mean: a
Darwinian evolutionary process in which memes, not
genes, evolve.
This paper is organised as follows. In Section 2 we
define embodied imitation and place this work in the
context of the research literature on robot imitation.
Then in Section 3 we describe the robots and infras-
tructure of the artificial culture lab. Section 4 describes
the robot–robot movement imitation algorithm at the
core of the Copybots, detailed in Section 5. Section 6
outlines the results from initial trials with robots. Fi-
nally Section 7 concludes the paper with discussion and
further work.
2 Embodied Imitation
We define embodied imitation as: the imitation of a
teacher-robot’s behaviour, or sequence of behaviours, by
a learner-robot, where the learner-robot uses only its
embodied sensors to perceive the teacher-robot. This def-
inition precludes robot–robot ‘telepathy’, i.e. one robot
transferring part of its controller directly to another,
and our insistence on embodied perception of one robot
by another means that an implementation of embodied
imitation needs to solve the so-called ‘correspondence
problem’; a term which refers to the learner’s problem
of translating a set of perceptual inputs to motor ac-
tions that correspond with the perceived actions of the
teacher [18].
The study of imitation and social learning in robots,
humans and animals has received cross-disciplinary at-
tention in recent years [19,17]. Not surprisingly much
attention has been given to the problem of humanoid
robots imitating humans, since this presents a way of
programming a robot by demonstration rather than
coding, see for instance [20, 14].
There has been less work describing experiments in
embodied robot-robot imitation. The earliest is per-
haps the work of Hayes and Demiris which describes
an approach with one (pre-programmed) robot finding
its way through a maze and another following it and
observing its actions (turns). The following (learner)
robot then associates each observed action with its own
(time delayed) perception of the environment and hence
learns how to navigate the maze, by imitation; this kind
of imitation is called ‘matched dependent behaviour’
[11]. Dautenhahn’s seminal 1995 paper for the first time
proposed a larger context of social interaction between
embodied robots, in which a similar approach to imita-
tion, i.e. one robot learning by following another, played
a part [6]. Following a connectionist approach Billard
and Hayes proposed the DRAMA architecture (Dynam-
ical Recurrent Associative Memory Architecture); they
provide one case study that interestingly involves the
active participation of the teacher robot in the process
of imitative learning [4].
Following their 1994 work, [11] Demiris et al, went
on to propose the HAMMER architecture (Hierarchical,
Attentive, Multiple Models for Execution and Recogni-
tion). In an important series of papers Demiris et al, de-
veloped an imitation architecture based upon the build-
ing block of paired inverse and forward models; the in-
verse model outputs motor commands but, instead of
actually driving the motors, those commands are fed
to the forward model and the output of the forward
model compared with the input of the inverse model.
Thus the robot is able to internally ‘rehearse’ possible
On Embodied Memetic Evolution and the Emergence of Behavioural Traditions in Robots 3
actions and compare these with its perception of the
actions it is trying to imitate [8, 12, 9].
Alissandrakis et al, developed the ALICE architec-
ture (Action Learning via Imitation between Corre-
sponding Embodiments) in order to address the prob-
lem of robot-robot imitation across dissimilar embod-
iments; although not tested with real robots, ALICE
contributes a powerful generalised solution to the corre-
spondence problem for agents (or robots) with different
morphologies [1,3, 2]. ALICE works by creating a corre-
spondence library relating the actions (and importantly
effects) of the teacher to actions (or action sequences)
that the learner is capable of.
3 The Artificial Culture laboratory
The artificial culture lab comprises a physical space
(arena) designed for and populated by miniature wheeled
mobile robots. The arena is closed in the sense that
its physical boundaries define the edges of the robots’
world, out of which they cannot physically stray. The
arena is open to the environment, thus robots (since
they have both light and sound sensors) are affected by
ambient lighting or noise levels. Providing that these ex-
ternal environmental influences do not overwhelm the
robots’ sensors, they are not a problem. Indeed, a low-
level of background ‘noise’ in the environment, for in-
stance local variations in light levels, may usefully con-
tribute to imperfect robot-robot imitation.
We make use of the well known e-puck robots [16].
Importantly, the e-puck robots can sense and track the
movements of other robots nearby (albeit imperfectly
because of their limited sensors); thus robots have the
physical means for imitation. They have multi-coloured
programmable lights (LEDs), simple cameras; micro-
phones and speakers giving a wide range of options
for robot–robot interaction. Robots can signal to each
other with movement, light, or sound, one-to-one or
one-to-many. Despite its clear strengths, the basic e-
puck lacks the computational power for the image pro-
cessing needed in vision based imitation and, to over-
come this limitation, we have designed an open-hardware
Linux extension board for the e-puck, based on the 32-
bit ARM9 microcontroller [13]. The extension board
also provides WiFi communication, essential for moni-
toring and data logging, and Player [10] integration to
facilitate code development.
The artificial culture lab is fully instrumented. A vi-
sion tracking system from ViconTM 2 provides high pre-
cision position tracking. A dedicated swarm-server com-
bines the tracking data from the Vicon system with sta-
2(http://www.vicon.com)
tus information, such as internal state data, from robots
(via the WiFi network) and saves the experimental logs
for offline analysis and interpretation. Fig. 1(a) shows
the artificial culture lab arena in the Bristol Robotics
Lab (BRL); Fig. 1(b) shows one of the e-puck robots fit-
ted with Linux extension board, red skirt and tracking
‘hat’.
4 Robot–robot imitation of movement
We are concerned here with the embodied imitation of
behaviour, but ‘behaviour’ is too broad a term. Within
embodied imitation we can identify at least three types
of imitation:
imitation of actions only, i.e. one robot copying an-
other’s sequence of movements, sounds or lights;
imitation of action and perception, i.e. one robot
copying another’s interactions with objects or other
robots: we label this the ‘imitation of interaction’
and it is distinct from the imitation of actions be-
cause it requires that the learner-robot infers how
changes to sensory inputs trigger actions from ob-
servation of the teacher-robot;
imitation of goals, i.e. one robot copying the goals
or intentions of another using, perhaps, a completely
different set of actions.
Because it is the simplest we have first implemented
the imitation of actions, and specifically the imitation
of movement. The second, imitation of interaction, and
third, imitation of goals, are outside the scope of this
paper but will be considered as further work. We now
describe the imitation-of-movement algorithm and ex-
perimental results obtained.
Before outlining the imitation algorithm we first
need to describe the basic setup and some simplifying
assumptions. In this approach the teacher-robot per-
forms a sequence of movements while the learner-robot
watches it and attempts to learn the observed sequence.
The roles of teacher and learner are not fixed but in-
terchangeable and – since we are interested in propaga-
tion of imitated behaviours – robots alternate between
teacher and learner modes. In teacher mode when a
robot is ready to perform a movement sequence it will
first signal this by flashing its red LEDs. After complet-
ing the movement sequence the teacher-robot will sig-
nal again with its red LEDs. The learner-robot remains
stationary while observing, only turning on-the-spot if
necessary to keep the teacher-robot in its field of view.
The learner-robot watches the teacher robot with its
onboard camera and, in order to facilitate the recogni-
tion of the teacher-robot and its movements, robots are
4 Alan FT Winfield, Mehmet Dincer Erbas
(a) (b)
Fig. 1 (a) Artificial culture lab showing 6 robots in the arena. (b) An e-puck with Linux board fitted in between the e-puck
motherboard (lower) and the e-puck speaker board (upper). Note both the red skirt, and the yellow ‘hat’ (which provides a
matrix of pins for the reflective spheres which allow the tracking system to identify and track each robot).
fitted with coloured skirts that contrast with the back-
ground (i.e. arena boundaries), as shown in Fig.1(b).
Since robots have only one camera and hence mono-
scopic vision the learner robot must judge the rela-
tive direction of movement and distance of the teacher
robot by tracking the position and size of the teacher’s
coloured skirt in its field of view. Although estimat-
ing relative size and position of the teacher robot is
straightforward, it is error prone because of the rela-
tively low resolution camera (640x480) and the presence
of other robots and, furthermore, the learner robot can-
not see the teacher robot’s turns – only infer them from
changes in direction, thus we simplify the correspon-
dence problem by limiting movement sequences to be
composed of on-the-spot turns (rotations) and straight
line segments at a constant speed. In the experiments
of this paper the straight line speed was fixed at 5.2
cm/second and turns take, on average, 1 second.
The imitation-of-movement algorithm thus has three
stages:
1. while observing captured visual frames, for each frame
estimate the relative position of the teacher robot,
storing these positions in a linked list;
2. after the teacher’s sequence is complete, process the
linked list using a regression line-fitting approach
to convert the estimated positions into straight line
segments (vectors);
3. transform the straight line segments, and their inter-
sections, into a sequence of motor commands (turns
and moves).
The imitation-of-movement algorithm outlined here
does not have the complexity of the architectures out-
lined above in section 2, although it does clearly share
a number of common elements. There are a number
of reasons for the relative simplicity of our approach.
Firstly, we are here imitating movement only and not
interaction with objects, or other robots: thus the learner
needs only to deduce action sequences and not perception-
action sequences. Secondly our robots are homogeneous
(similarly embodied), thus when the learner robot trans-
forms its estimate of the teacher robot’s movement tra-
jectory into ego-centric motor commands it can assume
it has the same motion dynamics as the teacher robot;
all robots move, while executing straight line segments,
at a constant velocity. Thirdly, we are interested pri-
marily in meme propagation across the robot collec-
tive, so our approach to imitation is only as complex
as needed to create the conditions for movement-meme
evolution.
5 Embodied memetic evolution: the Copybots
Fig. 2 shows the Finite State Machine (FSM) for our
initial trials in embodied memetic evolution. Each robot
runs the same FSM and we call these robots Copybots,
since they have no behaviours other than imitation [5].
The Copybots alternate between learner and teacher
modes. In teacher mode, on the right hand side of Fig. 2,
a robot progresses through three states:
On Embodied Memetic Evolution and the Emergence of Behavioural Traditions in Robots 5
Fig. 2 Finite State Machine for Copybots. Unlabelled tran-
sitions take place when the previous state completes (timings
are explained in the text). Different entry points for robots
starting in teacher or learner modes are shown. Once started
the FSM loops indefinitely, alternating between teacher and
learner modes.
1. Signal start of meme enaction. Here the robot lights
its red body LEDs for a pre-set time period (35 sec-
onds), to signal to other robots that it is about to
enact an imeme3from its memory. We call this the
‘attention’ signal.
2. Select and Enact meme. Firstly, the robot selects an
imeme from its memory for enaction (the choice of
selection operator is described below). Secondly, the
robot enacts the selected imeme by executing the se-
quence of turns and straight-line moves specified by
the imeme. The time spent in this state depends on
the number of turn-and-move pairs in the sequence
and the length of the moves. (As an example a move-
ment pattern which describes a square with 25 cm
sides will take about 24 seconds to complete.)
3. Signal end of meme enaction. Here the robot again
lights its red body LEDs for a fixed pre-set time
period (1.6 seconds), this time to signal that meme
enaction is complete (the ‘end’ signal). After com-
pleting this action the robot exits teacher mode and
enters learner mode, state 4.
In learner mode, on the left hand side of Fig. 2, a
robot progresses through two states:
3We use ‘imeme’ as shorthand for ‘internal representation
of a meme’.
4. Scan for attention signal. Here the robot scans for
another robot’s ‘attention signal’ by rotating and
scanning 360. When it sees the attention signal
(state 1 above) the robot transitions to the ‘track
and learn observed meme state’ described next.
5. Track and learn observed meme. Here the robot
tracks the movements of the other robot that has
got its attention (rotating if necessary to keep it in
its field of view), executing the algorithm described
in Section 4. The robot will continue to track un-
til it sees the ‘end’ signal (state 3 above), at which
point it will complete the process and store the new
learned meme in its memory. The robot will then
exit learner mode and enter teacher mode, state 1.
In order to coordinate the behaviour of teacher- and
learner-robots while at the same time allowing robots to
alternate between these states we arrange that robots
are organised at the start of an experiment in pairs.
In each pair one robot starts in teacher-mode and the
other in learner-mode. The entry points to the FSM
for these two modes are shown in Fig. 2. This means
that while the teacher-robot (of the pair) is in state 1
and making the attention signal, the other robot (the
learner) is in state 4, scanning for an attention signal.
Since each robot runs the same FSM, which loops in-
definitely, then the two robots of the pair will alter-
nate between teacher and learner modes, each in the
other mode. Note also that in experiments with more
than one pair of robots it is perfectly possible for a
learner-robot to catch sight of the attention signal of
the teacher-robot of a different pair. We regard this as
a desirable side-effect of the attention–scanning mech-
anism of states 1 and 4 as it allows different teacher-
learner pairs to emerge and hence behaviours to prop-
agate across the entire robot collective.
Consider now the selection operator of teacher mode,
state 2, above. There are clearly many criteria that
could be used to select which stored imeme to enact
but, in initial experimental trials, we have chosen to
test operators that do not select for particular features
or characteristics of stored memes. We thus avoid an
explicit fitness function in order to allow for the possi-
bility of undirected, or open-ended memetic evolution.
Instead we apply simple probabilistic selection criteria,
defined as follows:
Always select the most recently learned meme. This
is, in effect, memoryless imitation.
Select from the meme list at random, but weighted
in favour of the memes judged to be seen most often.
Here not all memes are stored, only memes that are
judged to be new, i.e. greater than a threshold value
of similarity, are added to the memory.
6 Alan FT Winfield, Mehmet Dincer Erbas
Select from the meme list by choosing, at random,
with equal probability. Here we assume that all ob-
served memes are stored, regardless of their similar-
ity.
6 Experimental Results
We have to date conducted trials with 2 and 4 robots,
limiting ourselves initially to this small number of robots
in order to focus on understanding the fidelity of imita-
tion (variation) observed in embodied imitation, and
the effect of different simple selection operators. We
present here representative results of three trials, which
– in turn – test the three selection operators outlined
above. For each trial we show tra jectory plots gen-
erated from the Vicon tracking data (robot x,y posi-
tions) logged, together with robot internal state data,
by our swarm–server. We present brief qualitative re-
sults for the first two selection operators: select the
most recently observed meme, and random selection
with weighted probability. For the third selection opera-
tor, random selection with equal probability, we present
a more detailed analysis in which we define a quality
of imitation metric and then use the metric to quan-
titatively analyse the first two imitation events before
then tracking the history of movement-meme evolution
through the course of the experimental trial.
6.1 Two robots: Select most recently observed meme
In Fig. 3 we see a trajectory plot of a two robot exper-
iment in which each robot alternates between teacher
and learner, and enacts the most recently seen meme.
Initially e-puck 9 is in teacher mode, and e-puck 12 in
learner mode, and e-puck 9’s memory has been preloaded
with a movement sequence that describes a square with
sides of 25cm. The experimental trial illustrated in Fig. 3
takes about 20 minutes and consists of about twelve
complete cycles of the FSM in Fig. 2, i.e. six teacher–
learner imitation events per robot. It is important to
note that the robot trajectories in Fig. 3 are not con-
tinuous, with each robot stopping after each meme en-
action in order to scan for and then track the other
robot. A screen recording can be viewed or downloaded
from [22], which shows a ‘playback’ of the first 14 min-
utes of the trajectories in Fig. 3, in Stage [21], with
status information. Here we change colour each cycle
to facilitate analysis.
The annotation on Fig. 3 show the initial square (e-
puck 9), and the 1st, 2nd, and 3rd generation copies.
It is immediately clear that each successive copy in-
troduces new imitation errors, in both turn angles and
straight-line lengths, which accumulate and quickly re-
sult in significantly distorted variants of the original
square. However, analysis shows that the number of seg-
ments remains at four until the robots become too far
apart to see each other (and the experiment is halted),
thus there is an inherited characteristic in this very sim-
ple example of movement-meme evolution.
6.2 Four robots: Random selection with weighted
probability
Fig. 4 Trajectory plot: four robot movement-meme evolu-
tion in which only dissimilar memes are stored and meme
selection is random, weighted in favour of similarly observed
memes. The four e-pucks are organised as two pairs: e-pucks
9 and 12, and e-pucks 29 and 32. At the start of the exper-
iment e-pucks 9 and 29 are initialised in teacher mode and
e-pucks 12 and 32 in learner mode.
In the trajectory plot of Fig. 4 we see four robots or-
ganised as two pairs: e-pucks 9 (purple) and 12 (green)
are initialised with a movement pattern which describes
a square trajectory and e-pucks 29 (red) and 32 (blue)
initialised with a closed 4-segment L-shaped pattern.
This experimental trail differs from those above in that
here we have constrained the movement-imitation al-
gorithm (both in estimating the turn angles, and in
enacting movements) to multiples of 90. The effect of
this constraint is evident in the qualitatively high fi-
delity copies of both square and L-shaped movement
patterns. What is, however, interesting is that robots
in the 9/12 pair have, from time to time observed and
stored the meme patterns from the 29/32 pair, and vice-
versa. Because of the weighted selection criterion the
On Embodied Memetic Evolution and the Emergence of Behavioural Traditions in Robots 7
Fig. 3 Trajectory plot: two robot imitation. The experiment starts with e-puck 9 in teacher mode, following a movement
trajectory that describes a square with sides of 25cm; e-puck 12 is initialised in learner mode.
odds are against one of these being selected and enacted
but, nevertheless, we see a square pattern enacted by
e-puck29 (lower left) and an L-shaped pattern enacted
by e-puck9 (upper right).
6.3 Two robots: Random selection with equal
probability
6.3.1 A quality of imitation metric
In order to quantitatively assess the fidelity of imita-
tion (i.e. similarity of learned memes) we need to define
a quality-of-imitation function, Qi. Since movement-
memes consist of a series of turn and straight line seg-
ments (vectors) we can compare the similarity of two
memes by separately estimating three quality indica-
tors: quality of angle (turn) imitation, quality of length
imitation, and quality of segment imitation. In effect we
decompose each movement-meme into its constituent
turn angles, straight-line move lengths and number of
straight-line segments. The quality of angle imitation
between original meme (O) and learned meme (L) is
calculated as follows:
Qa= 1 Pm|aL
maO
m|
PmaO
m
(1)
where amis the turn angle of move m, in degrees.
Here we determine the ratio of the sum of angle differ-
ences between the moves of original and learned memes,
to the total turn angle of the moves of the original
meme. If original and learned memes have a different
number of segments, NOand NLrespectively, then we
sum only over the number of segments in the smaller:
min(NL, N O). A value of 1 indicates perfect fidelity
imitation. The quality of length imitation similarly cal-
culates the length errors between original and learned
memes:
Ql= 1 Pm|lL
mlO
m|
PmlO
m
(2)
where lmis the length of move m, in mm. Again a value
of 1 indicates perfect fidelity imitation. The quality of
segment imitation simply considers the difference be-
tween the number of segments (vectors) between origi-
nal and learned memes:
Qs= 1 |NLNO|
NO(3)
where NLand NOare the number of segments of learned
and original memes, respectively. We now calculate the
weighted sum of the three quality indicators, to arrive
at a composite overall quality-of-imitation score:
Qi=AQa+LQl+SQs(4)
where A,Land Sare weighting coefficients, and A+
L+S= 1. In the results given here we choose to give
equal weighting to each of the three quality indicators,
thus A=L=S= 0.33.
6.3.2 Robot–robot imitation with variation
Fig. 5 shows two examples of embodied social learning,
of movement, by imitation. Each of the three subfigures
in Fig. 5 plots tracking data recorded, from the exper-
imental infrastructure described in Section 3, when an
e-puck robot enacts a single movement sequence. Here
e-puck 9 has been initialised with a sequence of three
turns and moves that describe an equilateral triangle,
with 15 cm sides, and Fig. 5(a) shows e-puck 9 enact-
ing the triangle. In this trial e-puck 12 watched e-puck
8 Alan FT Winfield, Mehmet Dincer Erbas
(a) (b) (c)
Fig. 5 (a) Meme 1: initial movement meme enacted by e-puck 9. (b) Meme 2: imitation of meme 1 by e-puck 12, Qi= 0.47.
(c) Meme 3: imitation of meme 2 by e-puck 9, Qi= 0.94. X and y axes are labelled in multiples of 0.1 mm and the circles
mark the start positions of each movement-meme.
9 enact the triangle and, using the procedure outlined
above, attempted to learn the movement sequence, by
embodied imitation; the result is shown in Fig. 5(b) and
it is immediately clear that this is a poor-fidelity copy.
Although the copy clearly retains characteristics of the
original triangle, i.e. the 3 longest line segments form
a triangle and intersect at angles close to 45, two ad-
ditional short segments have been inserted, one at the
start, followed by a u-turn, and another at the top apex
of the triangle. Given these two additional segments it
is not surprising that our quality of imitation score is
poor: Qi= 0.47. The quality of length imitation is much
higher: Ql= 0.75.
In this trial e-puck 9 then watched Meme 2, enacted
by e-puck 12, and attempted to learn it, thus Fig. 5(c)
is an imitation of Fig. 5(b). In contrast with the poor fi-
delity Meme 1 Meme 24imitation, we see that Meme
2Meme 3 imitation is much higher fidelity. Meme 3
is of course rotated with respect to Meme 2, but that
is exactly what we would expect. Meme 3 retains the
rather complex five segment structure of Meme 2, and
gives a very high quality of imitation score of Qi= 0.94;
e-puck 9 has certainly learned the complex ‘dance’ of e-
puck 12. We have thus demonstrated both robot–robot
social learning, by imitation, and shown that we obtain
variation in socially learned behaviours ‘for free’ as a
consequence of embodiment.
The question of precisely why the first imitation
here, Meme 1 Meme 2, was of much lower fidelity
than the second, Meme 2 Meme 3, is hard to answer.
However, there are several factors at work. One is that
the seeded movement pattern, the triangle, was cho-
sen arbitrarily and without regard to which movement
patterns may be easy or hard for the robots to copy.
We must not assume that any pattern we choose can
be imitated with high fidelity since the robots physical
4We use A B as shorthand for B is a learned and en-
acted copy of A.
and sensory morphology, and imitation algorithm, will
almost certainly favour some patterns over others; this
question is the subject of further work. Another factor
is ambient environmental variation - it is possible that
changes in light level across the arena made it harder for
e-puck 12 to see e-puck 9 than vice-versa. Such contin-
gencies are inevitable in embodied experiments of this
nature. Furthermore, the fact that the imitation algo-
rithm must infer turns by looking for the intersection
of straight lines fitted to discrete estimated positions
(as outlined in Section 4), combined with errors in es-
timating the position of the teacher-robot, may well be
responsible for imitation artefacts such as the straight
line segment inserted into the apex of the triangle at
the top of Fig. 5(b).
6.3.3 Towards open-ended memetic evolution
Fig. 6 plots the position data captured during a two
robot experiment in which each robot alternates be-
tween teacher-mode and learner-mode. Each robot learns
and stores the meme enacted by the other, but then –
when in teacher-mode – chooses which meme to enact
using the equal-weighting random-selection operator.
For clarity each movement sequence is shown here in
a different colour, and labelled with the order in which
the movement-memes were enacted by the two robots.
In this run each robots memory is initialised with one
imeme: a pattern of movements that describe an equi-
lateral triangle with sides of 15 cm, and e-puck 9 is ini-
tially in teacher mode. The plot in Fig. 6 is a screen cap-
ture from a tool that we have developed for Stage [21],
which ‘plays back’ the trajectories recorded from the
real-robot experiments. In this tool we change colour
each cycle to facilitate analysis. The screen recording
from which Fig. 6 was captured (and then annotated)
may be viewed or downloaded from [23].
On Embodied Memetic Evolution and the Emergence of Behavioural Traditions in Robots 9
Fig. 6 Trajectory plot: two robot movement-meme evolution in which all observed memes are stored and meme selection is
random, with equal probability. The experiment starts with e-puck 9 (left) in teacher mode, following a movement trajectory
that describes a triangle with sides of 15 cm.
We now apply the graphical meme-tracking approach
proposed in [24], in order to trace the evolution of memes
in the experiment of Fig. 6. Inspection of Fig. 6 shows
that a ‘figure of eight’ meme appears to dominate (movement-
memes 2, 3, 4, 6, 8, 9 and 13), and the meme evolution
diagram in Fig. 7 explains why.
Fig. 7 shows the evolution and heredity of memes
in the two robot experimental trial of Fig. 6. It does
not identify robots, but instead traces the evolution of
memes – something which is not obvious from the tra-
jectory plot of Fig. 6. To create Fig. 7 requires us to
analyse the recorded experimental logs of each robot’s
activity, step by step, in order to link the stored imemes
of the 2 robots; in other words determine for each learned
imeme, in the memory of each robot, which imeme of
the other robot it is a copy of. Thus, each horizontal
grey line in Fig. 7 represents a timeline for each sin-
gle imeme. When that imeme is selected and enacted
there are two possibilities: one is that the enaction was
not, at any time during the experimental trial, imi-
tated (i.e. learned and enacted) – these are shown as
crosses (and labelled in the key ‘enaction only’). The
other possibility is that the enaction was imitated dur-
ing the experimental trail – these are shown as blue ar-
rows (and labelled in the key ‘enaction and imitation’).
The enaction only events (crosses) are labelled with
the meme-enaction number in trajectory plot Fig. 6;
the enaction and imitation events (blue arrows) are la-
belled with originating (parent) meme-enaction num-
ber, and learned meme-enaction number from Fig. 6.
Each enaction and imitation event is also labelled with
the quality-of-imitation score Qi. Note that each enac-
tion and imitation event results in a new imeme timeline
which continues throughout the trial. This reflects the
fact that our robots, in this experiment, have unlimited
imeme memories. If we instead had either a mechanism
for robots ‘forgetting’ imemes (according to some cri-
teria) or robots themselves ‘dying’, then some imeme
timelines would terminate.
Thus we see, in Fig. 7, that Meme 2 is a poor-fidelity
copy of Meme 1 (0.47) – the first ‘figure of eight’ move-
ment pattern. Significantly, Meme 3 happens to be a
high-fidelity copy of Meme 2 (0.94), and furthermore
there are no further enaction and imitation events orig-
inating from Meme 1 – just two enaction only events:
5 and 10. Thus, all second and later generation memes
have, as an ancestor, Meme 2. This fact, together with
the high-fidelity copy of Meme 8 Meme 13 (0.96)
means that Memes 2, 3, 4, 8 and 13 are all either the
same or very closely related and we label these Meme
group A. Consider now imitation event Meme 3
Meme 6, which appears to be relatively poor quality
(0.55). However inspection shows that Meme 6, which
has four segments, has lost the initial short segment of
Meme 3; if we ignore the first segment of Meme 3 and
re-calculate Qifor Meme 3 Meme 6, we obtain 0.91
– which more closely reflects the subjective similarity of
Memes 3 and 6. By chance imitation event Meme 6
Meme 7 has inserted a new short segment so that Meme
7 returns to five segments and, by similarly ignoring the
new segment in Meme 7 and re-calculating Qi, we ob-
tain 0.88. Thus we see that Meme group B is both quan-
titatively and subjectively similar to Meme group A,
with strongly inherited characteristics retained across
five generations of meme: 2 to 12. We now understand
10 Alan FT Winfield, Mehmet Dincer Erbas
Fig. 7 A visualisation of meme evolution within the (two) robot collective. At the start of the period just one movement-
meme (triangle) is present; horizontal lines represent the ‘life course’ of each meme from left to right. Events (enaction only or
enaction and imitation) are labelled with numbers, in blue, which correspond with memes in Fig. 6. Enaction and imitation
events (blue arrows) are labelled with the quality-of-imitation score. Meme group A comprises memes (2, 3, 4, 8, 9 and 13)
and meme group B is memes (6, 7, 11 and 12); memes are shown and labelled in Fig. 6.
why the emergent figure of eight movement pattern has
become dominant.
Of course this particular meme evolution is highly
contingent. The emergence of the same kind (‘species’)
of dominant ‘figure of eight’ movement memes is most
unlikely to happen again (and indeed, in repeat trials,
has not). But this is exactly what one would expect
of an embodied evolutionary process. Perhaps what is
surprising is that in an open-ended evolutionary system
one kind of meme becomes dominant (at least in this
particular trial) – but this is simply explained by the
fact that if there is a group of closely related memes in
the robots’ memories (because of high-fidelity learning)
then our equal probability random selection operator is
more likely to select one of these. Note also just how
important the initial few imitation events are to the
later evolution of the system; the happenstance initial
sequence of a poor-fidelity imitation event followed by
a high-fidelity imitation event strongly (although not
completely) determined the later evolutionary course
of our trial system. Again this is strongly characteristic
of an evolutionary system.
7 Discussion and further work
This paper has described a multi-robot laboratory for
experiments in embodied imitation and memetic evolu-
tion. The project, of which this work forms a part is,
at the time of writing, ongoing and it would be prema-
ture to draw any general conclusions with regard to the
project aims of illuminating the processes and mecha-
nisms for the emergence of artificial traditions across
a robot collective. However, we can at this stage claim
that embodied imitation does indeed give rise to meme
variation ‘for free’, in the sense that those variations
arise from both embodiment and the process of estima-
tion inherent in solving the correspondence problem.
The initial trials described in this paper demonstrate
promising memetic evolution.
We can also conclude that the choice of selection
operator is critical to our aim of demonstrating the
emergence and evolution of stable new behavioural tra-
ditions. Our experimental trials clearly show that if a
robot always copies the last thing it learned we have too
much variation, as one might expect. On the other hand
with a random selection operator weighted to favour the
most frequently seen memes we have too little variation.
On Embodied Memetic Evolution and the Emergence of Behavioural Traditions in Robots 11
The simpler random selection with equal probability
operator appears to give the best balance between too
much and too little variation.
Further work will:
run much longer trials to investigate the dynamics,
over time, of dominant meme-groups and convergent
evolution;
explore the relationship between embodiment, in-
cluding sensor characteristics and robot morphol-
ogy, and the fidelity of imitation and the nature of
variation, and address questions relating to the sta-
bility of meme transmission;
introduce additional low-level robot behaviours and
thus associate imitation with behaviours that have
utility;
extend the imitation algorithm to implement the im-
itation of interaction so that interactions between
robots can be imitated and propagated across the
collective, with richer ‘social learning’;
further explore the mechanisms of meme selection
together with environmental variation, in order to
model the spatial and temporal dynamics of meme
propagation across the robot collective and the pos-
sibility of the emergence of artificial traditions.
Acknowledgements This work is supported by the UK En-
gineering and Physical Sciences Research Council (EPSRC),
grant reference EP/E062083/1 and the authors gratefully ac-
knowledge project co-investigators and researchers. We addi-
tionally wish to acknowledge Wenguo Liu, designer of both
the e-puck Linux extension board and the Stage tool which
generated the attached movies, and Jean-Charles Antonioli,
developer of the data logging system. We are grateful to Su-
san Blackmore for suggesting the random selection operator
of section 6.3. Finally we are grateful to the anonymous re-
viewers for their detailed and helpful comments.
Open science data: all datasets from the experimental
trials in this paper may be downloaded from the project web
pages: http://sites.google.com/site/artcultproject/
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As memes can be used in transmitting cultural information between people, memes can also be used to transmit cultural and other information between robots. This chapter builds on Chap. 2 suggesting a formalism for robot knowledge and intelligence. Robot memes and regular memes are contrasted, with extensions added to robot memes to describe how robot memes can be shared between robots and among robots and humans. The use of memes in development of robot culture is described, as well as how the memes shared among robots can be used to increase robot knowledge and intelligence through learning, storage of knowledge, and human guidance. Also discussed is the notion of malevolent memes that can contribute to incorrect robot behavior and can serve as means for accidental or purposeful fault injection into communities of robots. Corrective measures for such memes are also considered.
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