Abstract
This chapter addresses the problem of coordinating the behavior of very large numbers of microrobots to assemble complex, hierarchically structured physical objects. The approach is patterned after morphogenetic processes during embryological development, in which masses of simple agents (cells) coordinate to produce complex three-dimensional structures. To ensure that the coordination mechanisms scale up to hundreds of thousands or millions of microrobots, the swarm is treated as a continuous mass using partial differential equations. A morphogenetic programming notation permits algorithms to be developed for coordinating dense masses of microrobots. The chapter presents algorithms and simulations for assembling segmented structures (artificial spines and legs) and for routing artificial neural fiber bundles. These algorithms scale over more than four orders of magnitude.
TopArtificial Morphogenesis
Morphogenesis as a Model
One might legitimately question whether it is even possible to coordinate millions of microscopic agents to assemble complex structures. Fortunately we have an existence proof in embryological morphogenesis, which coordinates billions or trillions of cells to assemble a complex, hierarchical body (Nüsslein-Volhard, 2008). Even a relatively simple animal has a large number of distinct tissues, organs, vessels, nerves, etc. that are physically structured in a complex and functional organization. Moreover, multicellular organisms are hierarchically organized from the cellular (and indeed nanoscale) level up to the macroscopic level. Beginning from a single cell, the developing zygote begins to organize itself, establishing poles and layers, and the progressing organization governs future development, so that the microscopic agents (the cells) create the structure that governs their own future behavior. Cells migrate, following chemical gradients, and create forces and pressures that help to shape the tissues. Under the influence of structured signals, cells differentiate into functionally distinct tissues. Thus, the development of the embryo provides an inspiring example of how microscopic agents can coordinate their mutual behavior to self-organize into an immensely complicated structure. Our goal in artificial morphogenesis is to mimic these processes for the self-assembly of complex, hierarchical artificial systems by massive microrobot swarms.
Key Terms in this Chapter
Spatial Frame of Reference: Synonymous with Eulerian frame of reference (q.v.).
Material Frame of Reference: Synonymous with Lagrangian frame of reference (q.v.).
Caudal: Referring to the tail or posterior part of a structure.
Change Equation: An equation expressing the change in a quantity over time that can be interpreted either as a differential equation in continuous time or as a difference equation in discrete time. The change operator is written AU67: Equation Editor 132 (uppercase eth ).
Eulerian Frame of Reference: An approach to continuum mechanics in which spatially distributed variables are associated with fixed locations in space. Also called spatial frame of reference .
Body: In the context of artificial morphogenesis (q.v.), a specific instance of a substance (q.v.) occupying a region of space, which may vary as determined by the behavior of its constituent particles. A massive swarm of microrobots is treated as a body.
Rostral: Referring to the head or anterior part of a structure.
Lagrangian Frame of Reference: An approach to continuum mechanics in which spatially distributed variables are associated with fixed particles in a fluid or other substance, which may be moving through space. Also called material frame of reference .
Morphogenesis: The development of three-dimensional physical form during the development of an embryo.
Morphogen: A substance that diffuses and governs morphogenesis (q.v.) by means of variation in concentration.
Artificial Morphogenesis: A process for assembling or generating physical structures modeled more or less closely on biological morphogenesis (q.v.).
Substance: In the context of artificial morphogenesis (q.v.), a class of infinitesimal particles with particular defined properties and behaviors (analogous to a class in object-oriented programming). Substances are used to define the behavior of particular kinds of microrobots. We distinguish physical substances , which represent the relatively fixed physical properties of agents (e.g., mass, size, sensors, actuators), from controllable substances , which represent the programmable aspects of agent behavior.