Swarm Robotics • 2nd Edition • Heiko Hamann

Swarm Robotics: A Formal Approach

How do you get large robot groups to coordinate reliably—without a central brain? This expanded second edition is a practical, theory-backed guide to designing swarms that scale, stay robust, and work beyond the lab.

Release March 7, 2026 Edition Thoroughly expanded Audience Graduate text + reference
Springer book page Amazon

Tempting promise: If you can describe local robot rules, this book helps you reason about the emergent global system—its performance, its failure modes, and its scalability—so you can build swarms that are not just clever, but deployable.

Cover: Swarm Robotics: A Formal Approach (2nd Edition) by Heiko Hamann

Why read this book?

As robot systems grow in scale and complexity, understanding how large groups of robots can coordinate themselves without centralized control is becoming a critical challenge across industries. This thoroughly expanded second edition offers a definitive and up-to-date introduction to Swarm Robotics, one of the most transformative technologies of the upcoming decade. Now twice the length of its predecessor, the book provides a comprehensive overview of the field, covering both fundamental principles and recent developments.

Swarm Robotics is poised to transform global industries, including logistics, agriculture, infrastructure, disaster response, environmental monitoring, and defense. This book prepares readers to understand and design such systems, addressing everything from basic concepts to practical engineering challenges.

It begins with key concepts such as self-organization and feedback loops, and then introduces methods for designing and analyzing large-scale robot systems. Readers are guided through essential swarm skills, including flocking, synchronization, and gossiping, along with various application scenarios like aggregation, pattern formation, task coordination, and collective construction.

The new edition features modern approaches to scalability, human-swarm interaction, bio-hybrid systems, AR-based interfaces, and secure, fault-tolerant swarm architectures using blockchain and software redundancy. It explores field robotics beyond the lab, utilizing airborne, underwater, and surface robot swarms, and highlights emerging trends such as minimal-computation swarms.

Additional chapters provide an in-depth look at modeling and formal design methods, such as rate equations and data-driven algorithm synthesis. A detailed chapter on collective decision-making presents models from control theory and biology. Rich with exercises and examples, this new edition serves as both a graduate-level textbook and an authoritative resource for researchers and professionals seeking a thorough and current understanding of swarm robotics.

Unique Selling Points

  • Provides a comprehensive and up-to-date introduction to swarm robotics, including fundamentals and the latest developments.
  • Equips readers to design and deploy scalable robotic systems with real-world relevance in logistics, agriculture, defense, and environmental monitoring.
  • Shows how to design and model a swarm robotic system, including relevant mathematical definitions and tools.

Links: Springer · Amazon

Table of Contents

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Release: March 7, 2026

1 — Introduction to Swarm Robotics Key ideas, motivation, and foundations
p. 1
  • 1.1 Initial Approach to Swarm Robotics p. 3
    • 1.1.1 What Is a Swarm? p. 3
    • 1.1.2 How Big Is a Swarm? p. 4
    • 1.1.3 What Is Swarm Robotics? p. 5
    • 1.1.4 Why Swarm Robotics? p. 8
    • 1.1.5 What Is Not Swarm Robotics? p. 11
  • 1.2 Early Investigations and Insights p. 11
    • 1.2.1 Communication p. 11
    • 1.2.2 Two Levels: Micro and Macro p. 12
  • 1.3 Self-Organization, Feedbacks, and Emergence p. 14
    • 1.3.1 Feedbacks p. 15
    • 1.3.2 Examples of Self-Organizing Systems p. 16
    • 1.3.3 Emergence p. 18
  • 1.4 Other Sources of Inspiration p. 19
  • 1.5 Homogeneous and Heterogeneous Swarms p. 21
  • 1.6 The Human Factor p. 21
  • 1.7 Implementations in Hardware and Software p. 22
    • 1.7.1 Example Tasks and Swarm Robotic Projects p. 23
    • 1.7.2 Future Civil Applications p. 24
    • 1.7.3 Future Defense Applications p. 25
  • 1.8 Further Reading p. 27
  • 1.9 Exercises p. 27
2 — Scalability Performance, density, overhead, and cross-domain analogies
p. 29
  • 2.1 Introduction p. 30
    • 2.1.1 Learning Objectives p. 30
    • 2.1.2 Guiding Questions p. 30
  • 2.2 Conceptual Foundations p. 31
    • 2.2.1 What Is Scalability? p. 31
    • 2.2.2 Swarm Density p. 33
    • 2.2.3 Coordination Overhead p. 33
    • 2.2.4 Individual Performance p. 34
    • 2.2.5 Key Question and Cooperation–Interference Tradeoff p. 34
  • 2.3 Empirical Observations p. 35
    • 2.3.1 Optimality and a Concave Function p. 35
    • 2.3.2 Example: Bucket Brigades p. 37
    • 2.3.3 Opportunities to Collaborate: When Bigger is Better p. 38
  • 2.4 Computational Models of Scalability p. 41
    • 2.4.1 Speedup and Throughput p. 42
    • 2.4.2 Amdahl’s Law and Gustafson’s Law p. 43
    • 2.4.3 Queuing Theory p. 45
    • 2.4.4 Universal Scalability Law (USL) p. 49
    • 2.4.5 Superlinear Scalability: A Dream Comes True? p. 52
  • 2.5 Swarm Robotics Models of Scalability p. 54
    • 2.5.1 Swarm Performance Model p. 55
    • 2.5.2 The SGF Model: Solo, Grupo, and Fermo p. 56
    • 2.5.3 Two-Phase Performance: Living on the Edge p. 60
  • 2.6 Analogies from other Fields p. 63
    • 2.6.1 Traffic and Flow p. 63
    • 2.6.2 Biology, Chemistry, and Human Groups p. 66
  • 2.7 Implications for Swarm Design p. 69
    • 2.7.1 Online scalability p. 70
    • 2.7.2 Robust scalability and congestion control p. 70
    • 2.7.3 Meta-scalability p. 72
    • 2.7.4 Scalability in communication technology p. 72
    • 2.7.5 Deployment scalability p. 73
  • 2.8 Further reading p. 74
  • 2.9 Exercises p. 74
3 — Short Introduction to Robotics Core robotics notions for swarm contexts
p. 81
  • 3.1 Introduction p. 81
    • 3.1.1 Learning Objectives p. 81
    • 3.1.2 Guiding Questions p. 82
    • 3.1.3 On robots p. 83
  • 3.2 Components p. 85
    • 3.2.1 Body and Joints p. 85
    • 3.2.2 Degrees of Freedom and Pose p. 85
    • 3.2.3 Effector p. 86
    • 3.2.4 Actuator p. 86
    • 3.2.5 Sensor p. 87
  • 3.3 Odometry p. 89
    • 3.3.1 Non-systematic Errors, Systematic Errors, and Calibration p. 90
    • 3.3.2 The Art of Map Making p. 91
    • 3.3.3 Excursion: Homing in Ants p. 91
  • 3.4 Kinematics p. 92
    • 3.4.1 Forward Kinematics p. 93
    • 3.4.2 Inverse Kinematics p. 94
  • 3.5 Control p. 95
    • 3.5.1 Trajectory Error Compensation p. 96
    • 3.5.2 Controllers for Swarm Robots and Agent Models p. 99
  • 3.6 Swarm Robot Hardware p. 101
    • 3.6.1 Mobile robots for the lab p. 101
    • 3.6.2 Modular robotics p. 106
    • 3.6.3 Unmanned Surface Vehicle (USV) p. 107
    • 3.6.4 Autonomous Underwater Vehicles (AUV) p. 108
    • 3.6.5 Flying drones p. 108
    • 3.6.6 Active matter systems: ‘robots’ out of control p. 108
  • 3.7 Further Reading p. 110
  • 3.8 Exercises p. 110
4 — Short Journey Through Nearly Everything A compact micro–macro tour
p. 115
  • 4.1 Introduction p. 115
    • 4.1.1 Learning Objectives p. 115
    • 4.1.2 Guiding Questions p. 116
  • 4.2 Finite State Machines as Robot Controllers p. 116
  • 4.3 State Transitions Based on Robot–Robot Interactions p. 117
  • 4.4 Early Micro-Macro Problems p. 119
  • 4.5 Minimal Example: Collective Decision-Making p. 119
  • 4.6 Macroscopic Perspective p. 120
  • 4.7 Expected Macroscopic Dynamics and Feedbacks p. 121
  • 4.8 Further Reading p. 123
  • 4.9 Exercises p. 123
5 — Skills and Scenarios of Swarm Robotics From core skills to canonical tasks
p. 125
  • 5.1 Introduction p. 126
    • 5.1.1 Learning Objectives p. 126
    • 5.1.2 Guiding Questions p. 126
  • 5.2 Seven Skills p. 127
    • 5.2.1 Collision avoidance p. 128
    • 5.2.2 Synchronization and desynchronization p. 129
    • 5.2.3 Counting p. 133
    • 5.2.4 Random motion p. 135
    • 5.2.5 Flocking and general collective motion p. 139
    • 5.2.6 Gossiping p. 145
    • 5.2.7 The anti-robot and ‘less is more’ p. 146
  • 5.3 Scenarios p. 149
    • 5.3.1 Aggregation and Clustering p. 149
    • 5.3.2 Dispersion p. 152
    • 5.3.3 Pattern Formation, Object Clustering, Sorting and Self-Assembly p. 153
    • 5.3.4 Collective Construction p. 160
    • 5.3.5 Collective Transport p. 162
    • 5.3.6 Collective Manipulation p. 164
    • 5.3.7 Implementation of flocking and collective motion p. 165
    • 5.3.8 Foraging and Distributed Source Seeking p. 168
    • 5.3.9 Collective tracking p. 170
    • 5.3.10 Division of Labor and Task Coordination p. 170
    • 5.3.11 Shepherding p. 174
  • 5.4 Catastrophic Collective Behavior p. 178
  • 5.5 Heterogeneous Swarms p. 179
  • 5.6 Further Reading p. 180
  • 5.7 Exercises p. 180
6 — Modern Approaches to Robotics for Swarms HSI, AR, security, field robotics, and more
p. 187
  • 6.1 Introduction p. 188
    • 6.1.1 Learning Objectives p. 188
    • 6.1.2 Guiding Questions p. 188
  • 6.2 Human-swarm Interaction and Animal-swarm Interaction p. 189
    • 6.2.1 Human-swarm Interaction p. 190
    • 6.2.2 Animal-swarm Interaction: Mixed Societies, Bio-Hybrid Systems, and Cyborgs p. 197
  • 6.3 Human-robot Interfaces and Augmented Reality for Swarm Robots p. 199
    • 6.3.1 Human-robot Interfaces: Swarm Robots as Display and Input Device p. 200
    • 6.3.2 Augmented Reality for Swarm Robots p. 201
  • 6.4 Software Frameworks, Programming Approaches, and Computational Onboard Power p. 203
    • 6.4.1 ROS 2: Software architecture and middleware for mobile robots p. 204
    • 6.4.2 Buzz: Dedicated programming language for swarms p. 205
    • 6.4.3 Shared memory for swarms p. 206
    • 6.4.4 Swarm robots with heavy onboard compute p. 207
  • 6.5 Swarm-SLAM, C-SLAM, and Distributed SLAM p. 208
  • 6.6 True Robustness, Fault Management, and Security p. 209
    • 6.6.1 True Robustness and Software Redundancy p. 209
    • 6.6.2 Fault Management and Change Detection p. 211
    • 6.6.3 Cybersecurity and Blockchains p. 214
  • 6.7 Field Robotics: Kicking the robots out of the lab p. 217
    • 6.7.1 Waterborne p. 218
    • 6.7.2 Airborne p. 221
    • 6.7.3 Groundborne p. 223
  • 6.8 Swarm behaviors without computation p. 223
    • 6.8.1 Swarm robots without computation p. 223
    • 6.8.2 Programming swarm robots by shaping them p. 224
  • 6.9 Green Robotics p. 225
  • 6.10 Multi-swarm Coordination p. 227
  • 6.11 Further Reading p. 228
  • 6.12 Exercises p. 229
7 — Modeling Swarm Systems and Formal Design Methods From rate equations to data-driven synthesis
p. 233
  • 7.1 Introduction p. 233
    • 7.1.1 Learning Objectives p. 233
    • 7.1.2 Guiding Questions p. 234
  • 7.2 Introduction to Modeling p. 235
    • 7.2.1 What Is Modeling? p. 235
    • 7.2.2 Why Do We Need Models in Swarm Robotics? p. 236
  • 7.3 Local Sampling p. 237
    • 7.3.1 Sampling in Statistics p. 238
    • 7.3.2 Sampling in Swarms p. 239
  • 7.4 Modeling Approaches p. 242
    • 7.4.1 Rate Equation p. 242
    • 7.4.2 Differential Equations for a Spatial Approach p. 245
    • 7.4.3 Network Models p. 250
    • 7.4.4 Network Science and Adaptive Networks p. 252
    • 7.4.5 Swarm Robots as Biological Models p. 254
  • 7.5 Formal Design Methods p. 254
    • 7.5.1 Multi-Scale Modeling for Algorithm Design p. 255
    • 7.5.2 Software Engineering and Verification p. 257
    • 7.5.3 Formal Global-to-Local Programming p. 258
    • 7.5.4 Simulation Tools p. 259
  • 7.6 Quick Overview of Data- & Search-driven Design Methods p. 261
    • 7.6.1 Automatic Design in Swarm Robotics p. 261
    • 7.6.2 Data-driven Design Methods p. 262
    • 7.6.3 Search-driven Design Methods p. 269
    • 7.6.4 Challenge of Reality Gap p. 275
    • 7.6.5 Modern Approaches for Robot World Models p. 276
  • 7.7 Further Reading p. 277
  • 7.8 Exercises p. 277
8 — Collective Decision-Making Models, tradeoffs, and implementations
p. 287
  • 8.1 Introduction p. 288
    • 8.1.1 Learning Objectives p. 288
    • 8.1.2 Guiding Questions p. 288
    • 8.1.3 From Individual to Collective Autonomy p. 289
    • 8.1.4 Next steps p. 289
  • 8.2 Decision-Making p. 290
  • 8.3 Group Decision-Making p. 291
    • 8.3.1 Group Decision-Making in Control Theory p. 292
    • 8.3.2 Group Decision-Making in Animals p. 293
  • 8.4 Challenges and Context of Collective Decision-Making p. 295
    • 8.4.1 Speed-vs-accuracy Tradeoff p. 295
    • 8.4.2 Technical and Algorithmic Challenges p. 296
    • 8.4.3 Embodied Geometry of Decisions p. 300
    • 8.4.4 Motion as a Decision Process p. 300
  • 8.5 Models for Collective Decision-Making Processes p. 301
    • 8.5.1 Urn Models p. 303
    • 8.5.2 Voter Model p. 309
    • 8.5.3 Majority Rule p. 309
    • 8.5.4 Cross-inhibition Model p. 310
    • 8.5.5 Bayes Bots p. 311
    • 8.5.6 Hegselmann and Krause p. 311
    • 8.5.7 Kuramoto Model p. 312
    • 8.5.8 Swarmalator p. 313
    • 8.5.9 Axelrod Model p. 315
    • 8.5.10 Ising Model p. 315
    • 8.5.11 Fiber Bundle Model p. 317
    • 8.5.12 Sznajd Model p. 318
    • 8.5.13 Bass Diffusion Model p. 318
    • 8.5.14 Sociophysics and Contrarians p. 319
  • 8.6 Implementations p. 321
    • 8.6.1 Decision-Making with 100 Robots p. 321
    • 8.6.2 Collective Perception as Decision-Making p. 323
    • 8.6.3 Aggregation as Implicit Decision-Making p. 325
  • 8.7 Further Reading p. 325
  • 8.8 Exercises p. 327
9 — Case Study: Adaptive Aggregation Biological inspiration → model → verification
p. 335
  • 9.1 Introduction p. 335
    • 9.1.1 Learning Objectives p. 335
    • 9.1.2 Guiding Questions p. 336
  • 9.2 Use Case p. 336
  • 9.3 Alternative Solutions p. 337
    • 9.3.1 Ad-hoc Approach p. 337
    • 9.3.2 Gradient Ascent p. 337
    • 9.3.3 Positive Feedback p. 338
  • 9.4 Biological Inspiration: Honeybees p. 338
  • 9.5 Model p. 339
    • 9.5.1 Modeling Aggregation: Interdisciplinary Options p. 340
    • 9.5.2 Spatial Model p. 341
  • 9.6 Verification p. 345
  • 9.7 Short Summary p. 346
  • 9.8 Further Reading p. 346
  • 9.9 Exercises p. 347
Epilogue Closing perspective
p. 353
  • Epilogue p. 353

Table of contents reproduced from the provided contents PDF.