This chapter addresses the problem of coordinating very large swarms of microscopic agents to assemble complex, hierarchically structured physical systems. The agents might be microscopic robots or genetically engineered microorganisms. The approach we use is a form of artificial morphogenesis, which studies the self-organized morphogenetic processes in the developing embryo, by which billions of cells cooperate to create physical form and abstracts these processes to control microscopic agents to assemble desired physical structures. We use an approach based on the description of morphogenetic processes by partial differential equations, which ensures that our morphogenetic algorithms will scale up to arbitrarily large swarms (millions or more). We present several simulation experiments demonstrating the coordination of massive swarms to construct complex objects.

Chapter Contents:

• Abstract
• 20.1 The challenge
• 20.1.1 Assembling complex hierarchical structures
• 20.1.2 Artificial morphogenesis approach
• 20.1.3 Distinctive properties of microscopic agents
• 20.1.4 Scalability
• 20.2 Massive swarms
• 20.2.1 Continuum mechanics approach
• 20.2.2 Mathematical framework
• 20.2.2.1 Intensive quantities
• 20.2.2.2 Balance equations
• 20.2.2.3 Lagrangian reference frame
• 20.2.3 Global-to-local compilation
• 20.3 Morphogenetic programming notation
• 20.3.1 Change equations
• 20.3.2 Substance definitions
• 20.3.3 Physical vs. controllable substances
• 20.3.4 Bodies
• 20.4 Examples
• 20.4.1 Fiber bundle routing
• 20.4.1.1 The U-machine
• 20.4.1.2 Modified flocking algorithm
• 20.4.1.3 Continuous version
• 20.4.2 Clock and wavefront process
• 20.4.2.1 Biological model
• 20.4.2.2 Spine assembly
• 20.4.2.3 Leg assembly
• 20.5 Conclusions
• Acknowledgment
• References

Inspec keywords: partial differential equations; biology computing; self-adjusting systems; genetic engineering; microorganisms; cellular biophysics; large-scale systems; multi-robot systems

Other keywords: physical systems; partial differential equations; microscopic agents; developing embryo; desired physical structures; self-organized morphogenetic processes; genetically engineered microorganisms; massive swarms; complex objects; microscopic robots; complex structures; artificial morphogenesis; physical form; coordinating swarms

Subjects: Cellular biophysics; General, theoretical, and mathematical biophysics; Function theory, analysis