Explicit and Implicit Directional Information Transfer in Collective Motion

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© 2012 Massachusetts Institute of Technology Articial Life 13: 551–577
[
Explicit and Implicit Directional Information Transfer in Collective Motion
E. Ferrante1,2, A. E. Turgut1,2, C. Huepe3, M. Birattari1, M. Dorigo1and T. Wenseleers2
1IRIDIA, CoDE, Universit´
e Libre de Bruxelles, 50 Av. Franklin Roosevelt CP 194/6, 1050 Brussels, Belgium
2Laboratory for Entomology, Katholieke Universiteit Leuven, 59 Naamsestraat - bus 2466, 3000 Leuven, Belgium
3Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL 60208, USA ]
Extended Abstract
We study the cohesive coordinated collective motion of a group of mobile autonomous robots. We use virtual interactions
between robots implemented via proximal control, which allows the robots to reach a stable formation using virtual potential
functions (Turgut et al., 2008; Ferrante et al., 2011). The alignment component can be seen as a mechanism for directional
information transfer (Sumpter et al., 2008). We refer here to information transfer in collective motion as the process through
which robot orientation is transferred to its neighbors over time.
We consider here two information transfer mechanisms for collective motion in a group of mobile robots. The first one
exploits information transfer through direct communication and requires robots equipped with proximity, orientation sensing
and communication devices. We propose communication strategies that allow the robots informed about a desired direction
of motion to influence the rest of the group (Couzin et al., 2005; Ferrante et al., 2011). The second mechanism consists
of information transfer without the alignment component and communication (Ferrante et al., 2012), which can be used on
simpler robots only equipped with proximity sensors. We developed a simple motion control mechanism that allows a group
of robots to perform collective motion in a random direction without needing robots informed about a desired direction or an
explicit alignment behavior: information among the robots is thus transferred indirectly.
Information transfer via communication We consider a case where some robots have a persistent desired direction of
motion (desired direction A) which could, for example, represent the direction to a food source. There is also a second desired
direction (desired direction B), only present during a time window which could, for example, represent the escape direction
from a predator. Desired direction Bis in conflict with A: it points in the opposite direction and has higher priority. The
objective is to move the group in the direction that, at a given time, has the maximum priority, and to keep the group cohesive.
We proposed a self-adaptive communication strategy (SCS), that is an extension of two previously proposed strategies (Fer-
rante et al., 2011). In SCS, the robot sends an angle ✓s0and receives angles ✓sifrom its kneighbors. It computes the average
of the received angles: h=Pk
i=0 ej✓si
kPk
i=0 ej✓sik. The angle sent is: ✓s0=6[wg+ (1 −w)h]. The parameter w2[0,1] is the degree
of confidence of the robot on the desired direction g. Non-informed robots use w=0(they possess no information about g).
Robots informed about desired direction Buse w=1, which makes them stubborn. Robots informed about desired direction A
increase wwhen they measure high level of consensus in the information received by the neighbors, and decrease it otherwise.
Figure 1a shows the distribution of the accuracy over time, which measures how close the group direction is to desired
direction A. In these experiments, 1% of the robots is always informed about desired direction A. During the time window
where an additional 1% of the robots is informed about desired direction B, the accuracy reaching 0indicates that desired
direction Bis being followed. In the remaining part of the experiment, the group correctly follows desired direction A. This
result has been validated on real robot experiments (Fig. 1b). In addition, we show that SCS results either in a better accuracy
(Fig. 1a and Fig. 1b) or in a better group cohesion (Fig. 1c) than two previously proposed strategies, HCS and ICS. The full
results are reported in Ferrante et al. (2011).
Information transfer without communication We study information transfer with no alignment behavior and no communi-
cation. Our approach is based on a novel Magnitude Dependent Motion Control (MDMC) method, used to compute the forward
and angular speed of the robot. The two speeds depend on the magnitude and angle of f, the vector resulting from proximal
control that encodes the attraction and repulsion strenght from the neighbors. fxand fydenote the projection of fon the axis
parallel (x) and perpendicular (y) to the direction of motion of the robot. In MDMC, the forward speed uis proportional to the
xcomponent: u=K1fx+U, and the angular speed !to the ycomponent: !=K2fy, where Uis a forward biasing speed.
Figure 1 (second row) shows the results of experiments performed with simulated and real robots. MDMC is compared to the
method used in Turgut et al. (2008): Magnitude Independent Motion Control (MIMC). In MIMC, the forward and angular speed
do not depend on the magnitude of the vector fbut just on its angle. Figure 1d shows the distribution of the order metric over
time, which measures the degree of alignment in the group. MDMC achieves ordered motion without the alignment behavior

0 500 1000 1500
0.0 0.2 0.4 0.6 0.8 1.0
time (s)
Accuracy
300 robots , 3 informed
HCS
ICS
SCS
(a)
0 50 100 150 200
0.0 0.2 0.4 0.6 0.8 1.0
time (s)
Accuracy
8 robots , 1 informed
HCS
ICS
SCS
(b)
HCS ICS SCS
0123456
300 robots , 3 informed
Communication strategy
Number of groups
(c)
0 500 1000 1500 2000 2500
0
0.2
0.4
0.6
0.8
1
Time
Order
1000 robots − No Alignment
MIMC
MDMC
(d)
0 50 100 150 200 250 300
0
0.2
0.4
0.6
0.8
1
8 robots − No Alignment
Time
Order
(e)
−5
0
5
MIMC 0.01
MDMC 0.01
MIMC 0.05
MDMC 0.05
MIMC 0.1
MDMC 0.1
MIMC 0.15
MDMC 0.15
MIMC 0.2
MDMC 0.2
100 robots − No Alignment
Traveled distance (m)
(f)
Figure 1: Experiments with simulated and real robots. Time dependent data is sampled every second. Black lines are the
medians of the distribution, whereas grey lines (in (a), (b)) and error bars (in (d), (e)) represent the 25% and the 75% quartiles.
and without informed robots, whereas MIMC does requires informed robots or the alignment behavior. These conclusions are
backed up by real robot experiments (Fig. 1e). Moreover, when a proportion of informed robots (0.01,0.05,0.1,0.15,0.2as
indicated in the plot) is introduced, the group is able to travel further along a desired direction of motion using MDMC than
using the earlier MIMC method (Fig. 1f).
Discussion and conclusion We showed that the information needed to achieve collective motion can be transferred either
directly or indirectly. Direct information transfer requires robots with orientation sensing and communication devices. We
developed a communication strategy that can cope with two conflicting desired directions of motion. We also proposed a
novel mechanism for robot motion that exploits indirect information transfer. This allows robots that lack the above mentioned
capabilities to perform cohesive collective motion without communication, showing that implicit information transfer on the
heading direction takes place even without communication. In future work, we will use information-theoretic metrics to measure
information transfer more rigorously.
Acknowledgements This work was partially supported by: the European Union (ERC Advanced Grant “E-SWARM”, contract 246939);
the F.R.S.-FNRS of Belgium’s French Community (Meta-X project); the Vlaanderen Research Foundation Flanders (H2Swarm project), the
US National Science Foundation (Grant No. PHY-0848755).
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Collective Dynamics Extended Abstracts
552 Articial Life 13