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?

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 www.scottcamazine.com

Physical Patterns www.scottcamazine.com

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?