1. Introduction to Self-Organization
Ari Requicha
Professor, CS and EE
Founding Director, Lab for Molecular Robotics
University of Southern California

2. 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?

3. 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.

4. Requirements for Self-Organization
Positive feedback - amplification of fluctuations
random walks
errors
instability
Negative feedback - system stabilization
saturation
exhaustion
competition
Multiple interactions among components

5. 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, ...

6. Animal Patterns

7. Botanical Patterns

8. Physical Patterns

9. Modeling Self-Organization Phenomena
Nonlinear differential equations.
Simulation.
Cellular automata (similar to “game of life”).

10. 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)

11. 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

12. Coordination Mechanisms
Self-organization.
Response thresholds: Stimulus > Threshold  Behavior.
Environmental patterns (“templates”, heterogeneities): Pattern  Behavior.
Stigmergy: environment pattern is created by the agents.

13. 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?