Table Of ContentSPRINGER BRIEFS IN COMPLEXITY
Roland Bouffanais
Design and
Control of Swarm
Dynamics
123
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Roland Bouffanais
Design and Control
of Swarm Dynamics
123
RolandBouffanais
Engineering ProductDevelopment
Singapore University of Technology
andDesign
Singapore
Singapore
ISSN 2191-5326 ISSN 2191-5334 (electronic)
SpringerBriefs inComplexity
ISBN978-981-287-750-5 ISBN978-981-287-751-2 (eBook)
DOI 10.1007/978-981-287-751-2
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To my beloved wife Ariane,
and our turbulent, chaotic,
and joyful swarm of boys:
Aurélien, Tristan, and Thibault
Preface
Inthepastdecades,scientistsandengineershavebeenfacedwiththedevelopment
and management of an ever-increasing number of distributed systems made of
many interconnected components: e.g., the Internet, integrated power grids, trans-
portation networks, cyber-physical systems, fleet of autonomous vehicles, etc. All
these systems are complex systems in the sense that they are dynamical systems
made of many interacting parts that under certain conditions give rise to sponta-
neousself-organization.Inmanycases,theiroverallcollectiveorganizationhasnot
been specifically designed but instead grew dynamically out of some needs and
requirements at the local level: e.g., local area networks, power grid extensions,
new road or airport developments, etc.
As humans,we are also becomingincreasinglymore interconnected: physically
thanks to transportation networks, and virtually with the advent of social net-
working platforms and associated practices. In addition, the unprecedented growth
ofdenseurbanenvironmentsledtotherealizationofthecrucialneedtocontroland
regulatedynamiccollectivebehaviors:betheyvehiclesontheroad,airplanesinthe
vicinity of airports, and even human crowds in high-density areas.
Throughself-organization,thesecomplexsystemsmadeupofartificialorliving
units are capable of collectively performing tasks that greatly outperform each
individualagent’sability.Thus,thewholebecomesgreaterthanthesumofitsparts
such that the group harnesses swarm intelligence to produce robust and flexible
collective actions. On the other hand, under certain conditions, these emergent
properties may trigger a disruptive process—often cascading and catastrophic—
such as a collapse in collective operation or cooperation, jamming, etc.
This book is about one specific class of complex systems, namely swarming
systems in the biological realm, or also multiagent networked systems in the
engineering realm. Swarms represent one of nature’s most sophisticated achieve-
ments in collective operation. As scientists, we are only starting to unlock the
secrets of the awe-inspiring dynamics and displays of biological swarms. As
engineers, we envision a future filled with specifically designed artificial swarms
vii
viii Preface
performing complex tasks with astonishing effectiveness, robustness, and
flexibility.
Devising control laws and design principles for artificial swarms requires a
thorough overarching understanding of swarms. This scientific endeavor is truly
interdisciplinary as elements from biology, physics, network science, complexity
theory,control,informationtheory,andcomputationarenecessary.Thisbookaims
at emphasizing the connections between all these disciplines in order to provide a
holistic approach toward the design and control of swarm dynamics.
Acknowledgments
This book and some of the research it contains would not have been achieved
without the generous support and funding from the SUTD–MIT International
Design Center, the Temasek Lab@SUTD (under the STARS project), the
Singapore National Research Foundation, and the Singapore MIT Alliance for
Research and Technology. I would also like to acknowledge the stimulating and
productive scientific discussions with past and present members of my research
group at SUTD, the Applied Complexity Group, and in particular: Xiaoying Zhu,
Mohammad Komareji, Yilun Shang, André Sekunda, Yoke Kong Kuan, David
Mateo, and Alex Zhukov.
Singapore Roland Bouffanais
July 2015
Contents
1 Complexity and Swarming Systems. . . . . . . . . . . . . . . . . . . . . . . . 1
2 A Biologically Inspired Approach to Collective Behaviors . . . . . . . 5
2.1 Collective Animal Behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Ethology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Why Biological Inspiration?. . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 What Nature Teaches Us About Swarming . . . . . . . . . . . . . . . . 8
2.4.1 Self-Organization and the Importance of Order in Life . . . 9
2.4.2 Positive Feedback and the Emergence of Order . . . . . . . . 11
2.4.3 Collective Behavior Without Large-Scale Order. . . . . . . . 12
2.4.4 Information Processing and Swarm Intelligence . . . . . . . . 13
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 A Physical Approach to Swarming . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 Self-Organization in Physicochemical Systems. . . . . . . . . . . . . . 17
3.1.1 Elementary Cellular Automata . . . . . . . . . . . . . . . . . . . . 18
3.1.2 Collective Phenomena in Physical Systems . . . . . . . . . . . 20
3.1.3 Collective Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 The Self-Propelled Particles (SPP) Model . . . . . . . . . . . . . . . . . 24
3.2.1 Dynamical Foundations. . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.2 Neighborhood of Interactions. . . . . . . . . . . . . . . . . . . . . 26
3.2.3 Dynamic Update Rule. . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 What Statistical Physics Teaches Us. . . . . . . . . . . . . . . . . . . . . 29
3.3.1 Phase Transitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.2 Scaling and Universality . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.3 Fluctuations, Correlations, Susceptibility,
and Nonapparent Collective Behavior. . . . . . . . . . . . . . . 33
3.3.4 Nonequilibrium Systems and Self-Organized
Criticality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
ix
x Contents
3.4 What the Theory of Dynamical Systems Teaches Us. . . . . . . . . . 36
3.4.1 Bifurcation, Catastrophe, Collapse, and Tipping Point. . . . 37
3.4.2 At the Edge of Chaos. . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 Inspiration and Swarm Design . . . . . . . . . . . . . . . . . . . . . . . . . 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 A Network-Theoretic Approach to Collective Dynamics. . . . . . . . . 45
4.1 A Science of Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Swarm Signaling Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Network Properties and Swarm Dynamics. . . . . . . . . . . . . . . . . 49
4.3.1 Assembling the Swarm Signaling Network . . . . . . . . . . . 49
4.3.2 Connectedness of the Signaling Network. . . . . . . . . . . . . 51
4.3.3 Shortest Connecting Path. . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.4 Clustering Coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.5 Degree Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.6 Resilience of Swarming. . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3.7 Controllability of Swarming. . . . . . . . . . . . . . . . . . . . . . 60
4.3.8 Swarm Network Dynamics . . . . . . . . . . . . . . . . . . . . . . 62
4.4 Design of Signaling Network for Artificial Swarming. . . . . . . . . 63
4.4.1 Models of Signaling Networks. . . . . . . . . . . . . . . . . . . . 64
4.4.2 Enhanced Swarming Behaviors . . . . . . . . . . . . . . . . . . . 68
4.4.3 Some Words of Caution . . . . . . . . . . . . . . . . . . . . . . . . 71
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5 An Information-Theoretic Approach to Collective Behaviors . . . . . 75
5.1 Social Information Transmission. . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 Role of Information in Collective Behaviors . . . . . . . . . . . . . . . 76
5.3 Information Flow in Swarms . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3.1 Quantifying Information . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3.2 Dynamics of Information Transfer . . . . . . . . . . . . . . . . . 78
5.3.3 Transmission Channels . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.4 Capacity of the Transmission Channel . . . . . . . . . . . . . . 81
5.3.5 Informational Bottlenecks in Collective Behaviors . . . . . . 82
5.3.6 Conditions for the Emergence of Collective Behavior
Under Data Rate Limitations . . . . . . . . . . . . . . . . . . . . . 83
5.3.7 Swarming Collapse Under Data Rate Limitations. . . . . . . 86
5.4 Information and Swarm Design . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4.1 Acquisition of Stimuli Information by the Swarm. . . . . . . 88
5.4.2 Dynamic Balancing of Positive and Negative
Feedback Loops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.4.3 Leveraging Technological Advances for Novel
Swarm Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
