Introduction to Self-Organization
Ari Requicha
Professor, CS and EE
Founding Director, Lab for Molecular Robotics
University of Southern California
http://www-bcf.usc.edu/~requicha
Motivation
 Nanorobots will be very small  Single robots will have limited
capabilities.
 Large numbers of nanorobots will be needed for achieving significant
goals.
 How should systems of such robots be designed and programmed?
 Can we learn from nature?
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Very Large Distributed Autonomous Systems
 Coordinated behavior: cooperation among many simple agents.
 Adaptive behavior: flexible and robust wrt external changes and
internal perturbations.
 Lack of central control: no supervision.
 Self-organization: complex global behavior emerges from simple
local interactions between agents or agents and the environment.
 Our biases:
– Construction of spatial patterns/shapes.
– Active systems such as robots or biological cells, not passive
such as molecules.
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Requirements for Self-Organization
 Positive feedback - amplification of fluctuations
– random walks
– errors
– instability
 Negative feedback - system stabilization
– saturation
– exhaustion
– competition
 Multiple interactions among components
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Characteristic Properties of Self-Organization
 Emergence of spatio-temporal patterns in an
initially homogeneous medium.
 Multiple stable states (attractors).
 Bifurcations: sudden transitions due to small
changes in parameters or initial conditions.
Self-organization is ubiquitous in nature: crystals,
clouds, shells, ... Studied in Physics, Chemistry,
Biology, ... Self-assembly is an interesting aspect,
now being studied in Nanotech, CS, ...
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Animal Patterns
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Botanical Patterns
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Physical Patterns
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Modeling Self-Organization Phenomena
 Nonlinear differential equations.
 Simulation.
 Cellular automata (similar to “game of life”).
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Example: Logistic Equation
Population model for organisms with non-overlapping generations.
 Nt = population at time (generation) t
 r = reproductive factor (~ how many children an individual has)
 Maximum population possible in the given environment = 1
 Population  [0, 1]
 Assumptions: population grows linearly with the number of individuals
while there are few; when the upper limit is approached, growth tapers
down to 0.
 Equation:
Nt+1 = r Nt (1 - Nt)
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Behavior of the Logistic Equation
 r<1N0
 1 < r < 3  N  Const
 3 < r < 3.4  Oscillation between 2 Attractors
 3.4 < r < 3.57  Oscillation between 4 Attractors
 r > 3.57  Chaotic behavior
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Coordination Mechanisms
 Self-organization.
 Response thresholds: Stimulus > Threshold  Behavior.
 Environmental patterns (“templates”, heterogeneities): Pattern 
Behavior.
– Stigmergy: environment pattern is created by the agents.
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Some Issues
 Coordination algorithms.
 Programming: What local rules are needed to achieve the desired global
behavior? “Global-to-local compilation”.
 Communication requirements. For ants: chemical cues, at very short
distances (usually contact). For nanorobots?
 Role of randomness.
 Performance evaluation
– How to include in optimization criteria robustness and adaptation?
– How to assess systems that depend on a multitude of parameters?
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