Swarm Intelligence – W12: Segregation, Aggregation, and ......Swarm Intelligence – W12:...

Swarm Intelligence – W12:Segregation, Aggregation, and Decision Processes I:

Social Insects, Sensor Networks, and Multi-Robot

Systems

Outline• An introduction to WSN• Collective decisions

– Common pattern– Natural examples– Mixed society examples– Artificial examples

• Aggregation and Segregation– Natural examples– Artificial examples

An Introduction to Wireless Sensor

Networks

Selected Slides from MOBICOM 2002 Tutorial T5

Wireless Sensor NetworksDeborah Estrin & Mani [email protected], [email protected]

UCLA

Akbar [email protected]

University of Wisconsin, MadisonCopyright © 2002

Intro

Embedded Networked Sensing Potential• Micro-sensors, on-board

processing, and wireless interfaces all feasible at very small scale– can monitor

phenomena “up close”

• Will enable spatially and temporally denseenvironmental monitoring

• Embedded Networked Sensing will reveal previously unobservable phenomena

Seismic Structure response

Contaminant Transport

Marine Microorganisms

Ecosystems, Biocomplexity

Source: D. Estrin, UCLA

Motivating Applications

App#1: Seismic• Interaction between ground motions and

structure/foundation response not well understood.– Current seismic networks not spatially

dense enough to monitor structure deformation in response to ground motion, to sample wavefield without spatial aliasing.

• Science– Understand response of buildings and

underlying soil to ground shaking – Develop models to predict structure response

for earthquake scenarios.• Technology/Applications

– Identification of seismic events that cause significant structure shaking.

– Local, at-node processing of waveforms.– Dense structure monitoring systems.

• ENS will provide field data at sufficient densities to develop predictive models of structure, foundation, soil response.Source: D. Estrin, UCLA

Field Experiment

⎜⎯⎯⎯⎯⎯⎯⎯ 1 km ⎯⎯⎯⎯⎯⎯⎜

• 38 strong-motion seismometers in 17-story steel-frame Factor Building.• 100 free-field seismometers in UCLA campus ground at 100-m spacing


App#2: Contaminant Transport• Science

– Understand intermedia contaminant transport and fate in real systems.

– Identify risky situations before they become exposures. Subterranean deployment.

• Multiple modalities (e.g., pH, redox conditions, etc.)

• Micro sizes for some applications (e.g., pesticide transport in plant roots).

• Tracking contaminant “fronts”.• At-node interpretation of

potential for risk (in field deployment).

Soil Zone

Groundwater

Volatization

SpillPath

Air Emissions

Dissolution

Water Well


Contaminantplume

ENS Research Implications

• Environmental Micro-Sensors– Sensors capable of

recognizing phases in air/water/soil mixtures.

– Sensors that withstand physically and chemically harsh conditions.

– Microsensors.• Signal Processing

– Nodes capable of real-time analysis of signals.

– Collaborative signal processing to expend energy only where there is risk.Source: D. Estrin, UCLA

App#3:Ecosystem MonitoringScience• Understand response of wild populations (plants and animals) to habitats

over time.• Develop in situ observation of species and ecosystem dynamics.

Techniques• Data acquisition of physical and chemical properties, at various

spatial and temporal scales, appropriate to the ecosystem, species and habitat.

• Automatic identification of organisms(current techniques involve close-range human observation).

• Measurements over long period of time,taken in-situ.

• Harsh environments with extremes in temperature, moisture, obstructions, ...


WSN Requirements for Habitat/Ecophysiology Applications

• Diverse sensor sizes (1-10 cm), spatial sampling intervals (1 cm - 100 m), and temporal sampling intervals (1 ms -days), depending on habitats and organisms.

• Naive approach → Too many sensors →Too many data.– In-network, distributed information processing

• Wireless communication due to climate, terrain, thick vegetation.

• Adaptive Self-Organization to achieve reliable, long-lived, operation in dynamic, resource-limited, harsh environment.

• Mobility for deploying scarce resources (e.g., high resolution sensors).


Enabling Technologies and Challenges

Enabling Technologies

Embedded Networked

Sensing& Actuation

Control system w/Small form factorUntethered nodes

ExploitcollaborativeSensing, action

Tightly coupled to physical world

Embed numerous distributed devices to monitor and interact with physical world

Network devices to coordinate and perform higher-level tasks

Exploit spatially and temporally dense, in situ, sensing and actuation


Sensor Node Energy Roadmap

20002000 20022002 20042004

10,00010,000

1,0001,000

100100

1010

11

.1.1

Ave

rage

Pow

er (m

W)

• Deployed (5W)

• PAC/C Baseline (.5W)

• (50 mW)

(1mW)

RehostingRehosting to Low to Low Power COTSPower COTS(10x)(10x)

--SystemSystem--OnOn--ChipChip--Adv Power Adv Power ManagementManagementAlgorithms (50x)Algorithms (50x)

Source: ISI & DARPA PAC/C Program

Communication/Computation Technology Projection

Assume: 10kbit/sec. Radio, 10 m range.Assume: 10kbit/sec. Radio, 10 m range.

Large cost of communications relative to computation Large cost of communications relative to computation continuescontinues

1999 (Bluetooth

Technology)2004

(150nJ/bit) (5nJ/bit)1.5mW* 50uW

~ 190 MOPS(5pJ/OP)

Computation

Communication

Source: ISI & DARPA PAC/C Program

New Design Themes• Long-lived systems that can be untethered and unattended

– Low-duty cycle operation with bounded latency– Exploit redundancy and heterogeneous tiered systems

• Leverage data processing inside the network– Thousands or millions of operations per second can be done using energy of

sending a bit over 10 or 100 meters (Pottie00)– Exploit computation near data to reduce communication

• Self configuring systems that can be deployed ad hoc– Un-modeled physical world dynamics makes systems appear ad hoc– Measure and adapt to unpredictable environment– Exploit spatial diversity and density of sensor/actuator nodes

• Achieve desired global behavior with adaptive localized algorithms– Cant afford to extract dynamic state information needed for centralized

control


From Embedded Sensing to Embedded Control

• Embedded in unattended “control systems”– Different from traditional Internet, PDA, Mobility applications – More than control of the sensor network itself

• Critical applications extend beyond sensing to control and actuation– Transportation, Precision Agriculture, Medical monitoring and

drug delivery, Battlefied applications– Concerns extend beyond traditional networked systems

• Usability, Reliability, Safety• Need systems architecture to manage interactions

– Current system development: one-off, incrementally tuned, stove-piped

– Serious repercussions for piecemeal uncoordinated design: insufficient longevity, interoperability, safety, robustness, scalability...


Sample Layered Architecture

Resource constraints call for more tightly integrated layers

Open Question:

Can we define anInternet-like architecture for such application-specific systems??

In-network: Application processing, Data aggregation, Query processing

Adaptive topology, Geo-Routing

MAC, Time, Location

Phy: comm, sensing, actuation, SP

User Queries, External Database

Data dissemination, storage, caching


WSN and SI

Two Main Application Categories

C1: Low-duty cycle continuous sampling (e.g., temperature/humidity field monitoring over years)

C2: Event-based monitoring (e.g., human, animal species monitoring, tracking) →probably the most appropriate one for SI algorithms since collaboration in a dynamic environment emphasized

WSN and SI• SI principles might have impact because:

– Volume/mass constraints and therefore limited resources at the individual node level

– Large number of nodes– Autonomy– Collaboration among nodes– Self-organization

• And might not have impact because:– Most of them assume underlying mobile systems– Most of them do not exploit direct communication– Most of them rely on full distributedness and often

centralization and synchronization means energy saving

Pointers on WSN• Mobicom 02 tutorial:

http://nesl.ee.ucla.edu/tutorials/mobicom02/• Course list:

http://www-net.cs.umass.edu/cs791_sensornets/additional_resources.htm• TinyOS:

http://www.tinyos.net/• Smart Dust Project

http://robotics.eecs.berkeley.edu/~pister/SmartDust/• UCLA Center for Embedded Networking Center

http://www.cens.ucla.edu/• Intel research Lab at Berkeley

http://www.intel-research.net/berkeley/• NCCR-MICS at EPFL and other Swiss institutions

http://www.mics.org

Collective Decisions

Modeling

Individual behaviorsand local interactions

Global structuresand collective

decisions

• Local rules and appopriate amplification and/or coordination mechanisms can lead to collective decisions

• Modeling to understand the underlying mechanisms and generate ideas for artificial systems

Ideas forartificialsystems

Understanding Collective Decisions

Choice occurs randomly

(Deneubourg et al., 1990)

Example 1: Selecting a Path (W2)

Example 2: Selecting a Food Source (W2)

• Leurre: European project focusing on mixed insect-robot societies (http://leurre.ulb.ac.be)

• Relevant Leurre partners for the presented work:

• ULB (coordinator, modeling, experimental work with insects/robots)

• Uni Rennes/CNRS (chemistry)• EPFL – ASL/LSRO (mobile robots design

and development)• EPFL – SWIS (vision-based tracking and

modeling)

Example 3: Selecting a Shelter

[Halloy et al., Science, Nov. 2007]

The LEURRE Project: OverviewGoal of the project: quantitatively characterize the self-organized collective decision-making process of a cockroach society by unravelling and influencing the local interaction rules

• A simple decision-making scenario: 1 arena, 2 shelters

• Shelters of the same and different darkness

• Groups of pure cockroaches (16), mixed robot+cockroaches (12+4)

• Infiltration using chemical camouflage and statistical behavioral model

The LEURRE Project: Sample ResultsLegend: mixed, pure; shelter 1, shelter 2

A . Symmetric shelters (infiltration) B. Asymmetric shelters (active control)

Macroscopic Model

Experiment

Experiment

The EPFL Tools for the LEURRE Project3. Multi-level modeling

Ss Sa

1

1

( 1) ( ) ( ) ( 1) ( ) ( ) ( )

( ) ( ) ( 1) ( )

join joinj j r s j j

leave leavej j

N k N k p N k j p j N k p j N k

p j N k j p j N k j−

+

⎡ ⎤+ = + − −⎣ ⎦− + +

Module-based microscopic model

Agent-based microscopic model

Macroscopic model

[Correll et al., ALife J., in prep.]

Ss SaSs Sa

Target system

1. Robots as a flexible, interactive, societal “microscope”

[Asadpour et al., ARS J., 2006]

2. A marker-less vision-based tracking tool: SwisTrack

[Correll et al., IROS 2006]http://sourceforge.net/projects/swistrack

Example 4: Selecting a Shelter[Garnier et al., IEEE-SIS 2005]

• Alice II robots, 1 m arena size• 10 robots group size• Aggregation algorithm inspired by

cockroaches• 14+ cm shelter is able to host the whole

populationDifferent shelters

Shelter size [cm]

Equal sheltersDifferent shelters

Example 5: Selecting a Direction

Converging on the direction of rotation (clockwise or anticlockwise):• 11 Alice I robots• local com, infrared based• Idea: G. Theraulaz (and A. Martinoli); implementation: G. Caprari, W. Agassounon

Object Aggregation and Segregation -

Natural Systems

Cemetery Organization in the Ant Messor Sancta

Reduction of the spread of infection? Chretien (1996)

Corpse Aggregation in the Ant Messor Sancta

It defines a class of mechanisms exploited by social insects to coordinate and control their activity via indirect interactions and signs left in the environment.

• Stigmergic mechanisms can be classified in two different categories: quantitative (or continuous) stigmergy and qualitative (or discrete) stigmergy

Stimulus

Answer

S1

R1

S2

R2

S3

R3

time

S 4

R4

S 5

R5

Stop

Definition

Stigmergy

A Microscopic Model of Corpse Aggregation

(Deneubourg et al. 1991)Characteristics of the algorithm for individual behavior

• When an ant encounters a corpse, it will pick it up with a probability which increases with the degree of isolation of the corpse

• When an ant is carrying a corpse, it will drop it with a probability which increases with the number of corpses in the vicinity

• Modulation of pick up/drop probabilities as a function of the pheromone clouds around the cluster -> quantitative (continuous)stigmergy

The probability that an agent which is not carrying an item will pick up an item

ppick-up =k1

k1 + f

Probability that an agent carrying an item will drop the item

pdrop =f

k2 + f

f: fraction of neighborhood sites occupied by object o (perceived stimulus)k1, k2: threshold constants

Algorithm for individual behavior

( )2

)2(

A Microscopic Model of Corpse Clustering

f

ppick-up1

0f = k1

0.25

f

1

00.25

pdrop

f = k2

Example in StarLogo (Termites)

Key ideas:• A sorting problem implies two or more objects

to be manipulated• Sorting = aggregation of the same type of

object and separation of different types of objects in different clusters

• Clustering = special case of aggregation and separation with one object type (so no separation)

From Clustering to Sorting

t = 15

t = 0

Short term memoryat t = 15

Probability of picking up an object of type i:

Probability of dropping an object of type i which is being carried:

f(oi): fraction of neighboring sites occupied by objects of the same typeof the object oi

k1, k2 : threshold constants

ppick-up(oi)= ( k1 / (k1 + f(oi) ) ) 2

pdrop(oi)= ( f(oi) / ( k2 + f(oi) ) 2

Individual behavioral algorithm

Clustering & Sorting

In this algorithm f(oi) are estimated based on a short-term memory tuned to the underlying random walk!

Perceptual field of an ant

(Deneubourg et al. 1991)

Results of the C&S Algorithm

What do these Simple Microscopic Models Explain?

• Explanation of cemetery organization in Lasius niger, Pheidole pallidula, and Messor Sancta ant species ok

• Explanation of brood sorting in Leptothorax ants (concentric annular sorting) unexplained! → a further mechanism should be involved → work with robots at UWE (Nigel Franks, Chris Melhuish) provide a better explanation (though not a definitive one probably)

Object Aggregation and Segregation -

Artificial Systems

The mission:From local actions to global tasks: stigmergy and collective robotics.

The plan:• Give the robot some means of moving some discrete items.• Give it a start by enabling it to make small clusters.• Think of some way of estimating local density so that it can use

the Deneubourg algorithm to make progressively larger clusters.

Solution:• Use quantitative stigmergy via physical cluster size as positive

feedback; positive feedback “embedded” in the system design

Puck Clustering (Beckers, Holland, and Deneubourg, 1994)

The behavior:


How does it works?• adding a puck to a cluster increases its size • taking a puck from a cluster reduces its size

• probability of leaving a puck on a cluster increases with the size of the cluster• probability of taking a puck from a cluster decreases with the size of the

cluster→ so rate of growth increases with size and the feedback is always positive

• The sum of the rates of growth over all clusters will be zero (conservation of pucks)

• Therefore the rate of growth of at least the smallest cluster must be negative• Probability of creating a new cluster in the middle of the arena and split a

cluster is zero• So the # of clusters is monotonically decreasing (but not strictly

monotonically decreasing) over time


Why a single cluster?

• Clusters of 2 or less pucks are irreversibly eliminated (“sharper”, more discontinuous function than that used by ants in the lower number of objects)

• Noise play a major role: good randomness in trajectories and “mixing up” through local interactions → asymmetric noise on the cluster size → the higher the ratio robots/pucks the higher the noise amplitude on cluster size

• Without microscopic noise the clustering process would risk to get stuck in a multi-cluster situation (as in the case of ant experiments)


Conclusion• Robots can form clusters using a simpler algorithm than that proposed

by Deneubourg for ants: – strictly local sensing without memory still work– no need of modulation of pick-up/dropping probabilities via an additional

modality (in ants, chemical communication); local stochasticity (summarized in agent probabilistic response in biological models) achieved “for free” via direct “mechanical interaction” with the objects

• The ant algorithm is robust: even when run on completely different platforms such as robots, it shows coherent behavior; it is robust to different underlying randomness forms, individual failures, interferences, and environmental disturbances.

• The algorithm could be improved in its efficiency … moving beyond natural frontiers on specific tasks!


Puck Clustering Modeling• Same microscopic modeling method explained in week 8;

no free parameters• From controller blueprint + geometrical considerations,

calculate the probabilities of finding teammates, clusters of a given size, walls and those of shaving pucks from a given cluster

• Consider typical delays for obstacle avoidance or manipulation maneuvers

• Different from stick pulling: environment is characterized by more states, more variety of interaction with a cluster than with a stick (dependent on the approaching angle)

Cluster Interaction ProbabilitiesReal robots Interaction Probabilities

Results using a Microscopic Model• [Martinoli, Ijspeert, Gambardella, 1999]• No macroscopic model, no extension for segregation (yet …)

Frisbee Clustering and Sorting(Holland and Melhuish, 1998)

Bio-mimicking experiment: Leptothorax ants

• Live in cracks in rocks• Sort their brood• Perform nest migrations:

- find a new nest site- move the queen and brood there- build a surrounding wall- sort the brood

• Because of the 2D habitat and the interesting behaviors, ideal subjects for representing in a land-robotic form ... but they build with particles of grit thesame width as their bodies (“blind bulldozing”)... so we need ‘building materials’the same width as the robots – Frisbees

• Arena’s area is 1760 times the area of a robot: same order of magnitude as the ratio of the area of a Leptothorax nest to a single ant.

• Qualitative/feasibility rather than quantitative/efficiency study

The Robots

• 23 cm in diameter

• 3h battery autonomy

• Motorola 68332, 16 Mb RAM

• 4 continuous emitting IR proximity sensors

• Microswitch on the gripper (threshold between 1 and 2 frisbees), locking-unlocking frisbee operations controlled by an actuator

• Double optical sensor (color detection) for center and periphery color detection of the carried frisbee

Frisbee Gathering and Sorting(Holland and Melhuish, 1998)

Experimental set-up


Exp. 1: behavior for basic clustering

Rule 1:if (gripper pressed & Object ahead) then

make random turn away from object

Rule 2:if (gripper pressed & no Object ahead) then

reverse small distance make random turn left or right

Rule 3:go forward

Modified Beckers et al. basic behavior for rigid walls/robots!


Exp. 1: Results for basic clustering (10 robots, 44 frisbees)

8h 25 min, end criterium:90% offrisbees gathered(40)


Exp. 1: comparison with performance Beckers et al. 94

• Beckers et al. 1994: 81 pucks and 3 robots in 1h 45 min

• Holland et al. 1998: 40 frisbees and 10 robots in 8h 25 min

Why? No quantitative comparison, modeling up to date …

• Different arena’s area, different robot speed

• Cluster of 1 object (Holland ‘98) vs. cluster of 2 objects (Beckers ‘94) irreversibly removed

• Noise in cluster shape (compacity of the clusters)

• …


Exp. 2: Could we form clusters at the edges of the arena?

"It must be emphasized that a very large arena was necessary in Deneubourg et al's experiments to obtain "bulk" clusters: in effect, ants are attracted towards the edges of the experimental arena if these are too close to the nest, resulting in clusters almost exclusively along the edges."Eric Bonabeau, 1998

Test:• Vary the algorithm ok• Vary the sensors ok• Vary the arena size?


Exp. 2: Boundary clustering, algorithm


with probability pmake random turn away from object

else with probability (1-p)reverse small distance (dropping the frisbee)make random turn left or right


reverse small distance (dropping the frisbee)make random turn left or right

Rule 3:go forward

Algorithm modified:

Rule 1 probabilistic!


Exp. 2: Boundary clustering, parameter bifurcationprobabilityof retention p RESULTS

1.0 leads to a central cluster after 6 hours 35 minutes

0.95 leads to a central cluster, stopped when 2 main central clusters formed. Stopped ~2.5hours

0.9 leads to a central cluster, stopped when 2 main central clusters formed. Stopped ~5hours

0.88 1 cluster formed at edge. 40/44 at 9hrs 5m continued to be stable up to 11hrs 20min.

0.85 1 major cluster formed at edge and approx. 15 singletons around the periphery. stopped after 1110hours

0.8 1 major cluster formed at edge and approx. 15 singletons around the periphery. Stopped after 11hrs

0.5 All pucks taken to periphery (frame 8, 0hr40mins)but no single cluster formed Stopped at 11 hrs

0.0 All pucks taken to periphery (frame 3 0hr15m) but no single cluster formed. Stopped at 3hrs.


Exp. 2: Boundary clustering, parameter bifurcation

p = 0.0p = 0.5p = 0.8

p = 0.88p = 0.9p = 1.0


Exp. 2: Boundary clustering, sensory modification

Drop puck/Leave puck

Drop puck/Leave puck

wall

Mean 100.3 0

Pick up/Retain puck

Obstacle detection only with central sensor (instead of the 3 frontal sensors)!

p =100.3/180 = 0.56

But robot movements not really uniformlydistributed (trajectories, no wall following ) …


Exp. 2: Boundary clustering, sensory modification

Similar to p = 0.88 in the algorithmic version!


Exp. 3: The pull back algorithm


make random turn away from object


if plain thenlower pin and reverse for pull-back distanceraise pin

endifreverse small distance make random turn left or right

• Initial idea: change the compacity (pull back distance is a sensitive parameter) for speeding up aggregation process

• Robot behavior different with ring or plain frisbees


Exp. 3: The pull back algorithm, results (pullback distance 2.6 frisbees, 6 robots)

t = 0h00 t = 1h45 t = 8h05

Annular sorting like in Leptothorax ants!


Exp. 3: The pull back algorithm, results (pullback distance 2.6 frisbees, 6 robots, end criterium: first cluster of 20 frisbees)

Trial 1 2 3 4 5

Time in hours 7.58 2.75 25.3 11.7 4.50

Number of plains

11 12 11 10 12

High std dev

Low std dev


Conclusion• Similarly to Beckers et al. experiment, robots can form clusters using

a simpler algorithm than that proposed by Deneubourg for ants (no memory, only mechanical interaction)

• Similarly to Beckers et al. experiment, the ant algorithm is robust but its efficiency can be improved (cost?, what sensor modalities? com?) Several design choices for achieving the same microscopic (and therefore macroscopic) system behavior are shown: SW (control parameter) vs. HW (different number of sensors) → system modeling!

• Clustering & Sorting more interesting than clustering only from application point of view!

• Our multi-level modeling methodology could provide great guidance for designing an efficient sorting robotic system!


Robot Aggregation and Segregation

Robot Aggregation using Wireless Communication - Setup

[Correll & Martinoli, ICRA-CBW07]

• Eg. 2 clusters of 3 robots, 6 of 1 robot• Webots experiments using Alice II with

radio, 12 robots total• Arena diameter: 1 m• Communication range: 10 cm• Simplified com model

Real robotic node: Alice II with Zigbee-compliant com module

Robot Aggregation using Wireless Communication – Macroscopic Model

Control algorithm (inspired by cockroach experiments of Jeanson et al., 2004)

Robot Aggregation using Wireless Communication – Sample Results

Microscopic Module-Based model (Webots)• 1500 runs• sample time 10 s• 3 h (10800 s) per run

Macroscopic model

Conclusion

Take Home Messages• WSN represent a very promising technology for a number of

application• Commonalities and synergies between swarm robotics, WSN,

and SI are potential there but need to further outlined and formalized

• Collective decisions can be taken by exploiting self-organization as key coordination mechanism (positive feedback necessary to reach consensus)

• Collective decisions can be taken by natural, artificial, and mixed systems consisting of mobile or static nodes

• Aggregation and segregation are two basic behaviors which are highly parallelizable and widely spread out in natural systems

• Aggregation/segregation mechanisms are also underlying some collective decisions

• Modeling techniques help as usual to understand natural systems and transport ideas to artificial platforms

Additional Literature – Week 12Papers• Martinoli A., Ijspeert A. J., and Mondada F., “Understanding Collective Aggregation

Mechanisms: From Probabilistic Modelling to Experiments with Real Robots”. Special issue on Distributed Autonomous Robotic Systems, Dillmann R., Lüth T., Dario P., and Wörn H., editors, Robotics and Autonomous Systems, 29(1): 51-63, 1999.

• Martinoli A., Ijspeert A. J., and Gambardella L. M., “A Probabilistic Model for Understanding and Comparing Collective Aggregation Mechanisms”. In Floreano D., Mondada F., and Nicoud J.-D., editors, Proc. of the Fifth European Conf. on Artificial Life, September, 1999, Lausanne, Switzerland, Lectures Notes in Computer Science, Springer Verlag, pp. 575-584.

• Wilson M., Melhuish C.; Sendova-Franks A. B.; Scholes S., “Algorithms for Building Annular Structures with Minimalist Robots Inspired by Brood Sorting in Ant Colonies”, Autonomous Robots, 17(2): 115-136, 2004.

• Scholes S., Wilson M., Sendova-Franks Ana B., and Melhuish C. “Comparisons in Evolution and Engineering: The Collective Intelligence of Sorting” Adaptive Behavior 12: 147-159, 2004.

• S. Garnier, C. Jost, R. Jeanson, J. Gautrais, A. Grimal, M. Asadpour, G. Caprari, and G. Theraulaz. The embodiment of cockroach aggregation behavior in a group of micro-robots. Artificial Life. Accepted for publication.

• Correll N. and Martinoli A., “Modeling Self-Organized Aggregation of a Swarm of Miniature Robots. Proc. of the IEEE ICRA 2007 Workshop on Collective Behaviors inspired by Biological and Biochemical Systems, April 2007, Rome, Italy.

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