Introduction to Self-Organization Ari Requicha Professor, CS and EE Founding Director, Lab for...

Introduction to Self-Organization

Ari Requicha

Professor, CS and EEFounding Director, Lab for Molecular Robotics

University of Southern California

http://www-bcf.usc.edu/~requicha

Laboratory for Molecular Robotics

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?


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.


Requirements for Self-Organization

Positive feedback - amplification of fluctuations

– random walks

– errors

– instability

Negative feedback - system stabilization

– saturation

– exhaustion

– competition

Multiple interactions among components


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, ...


Animal Patterns

www.scottcamazine.com


Botanical Patterns



Physical Patterns



Modeling Self-Organization Phenomena

Nonlinear differential equations.

Simulation.

Cellular automata (similar to “game of life”).


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)


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


Coordination Mechanisms

Self-organization.

Response thresholds: Stimulus > Threshold Behavior.

Environmental patterns (“templates”, heterogeneities): Pattern Behavior.

– Stigmergy: environment pattern is created by the agents.


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?

Introduction to Self-Organization Ari Requicha Professor, CS and EE Founding Director, Lab for...

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