3. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Self-Organization
Definition
• Macroscopic patterns emerge from microscopic level
interactions, without the guidance of an outside source.
• The execution of the rules are based only on local
information, without reference to the global pattern.
4. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Self-Organization in Engineering
Application
• Tissue Engineering. Repair part of or whole tissues, such
as bone, blood vessels, skin and muscle.
• A framework for distributed multi-agent systems.
• The control of robotic swarms.
• Development of basic building elements for future systems
that are capable of self-organization, self-assembly,
self-healing and self-regeneration.
Advantages
• Advantages over traditional method: scalability,
decentralization, adaptability.
5. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Self-Organizing Shape Formation Algorithms
Amorphous Computing
• Massive faulty identical-programmed particles.
• Particles have local states and some memory capability.
Cellular Automata
• Discrete model of cells on a regular grid.
• The value of a cell changes according to predefined rules.
Swarm Intelligence
• Collective behavior of a large number of autonomous
simple agents.
• Agents follow simple rules and interact locally with the
environment.
6. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Limitations of Current Algorithms
Limitations
• Require special global initialization of the environment.
• The local primitives have a blueprint of the final shape.
• Experiment with local interaction rules and inspect the
outcomes, rather than starting with predefined global
outcomes.
Difficulties
• Completely eliminate global information from low level
primitives.
• ‘Reverse Engineer’ the local interaction rules that lead to
specified outcomes.
7. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Truly Local Algorithms
Benefits
• Benefit the system with scalability and parallelizability.
• Eliminate central points of failure by eliminating leaders.
Problems
• How to convey a global goal to low level interactions?
• What can we use paradigms for designing such
algorithms?
• How can we control such a self-organizing process?
8. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
What Can We Learn from Developmental Biology?
Biological systems are based on the collective behaviors of a
large number of simple and unreliable parts.
Morphogenesis and Chemotaxis
• Living cells self-organize into complex structures.
9. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
What Can We Learn from Developmental Biology?
Chemotaxis
• Cells emit accumulating
chemicals into the
environment.
• Neighboring cells detect
the overall chemical
concentration at their
surfaces.
• Cells respond to the
stimulus by moving in the
direction of the gradient
either towards or away
from the source.
• Cell movements produce
large-scale aggregation.
• The motions may lead to
complex pattern formation
or sorting of cells.
10. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Thesis
Biologically-Inspired Algorithms for Spatial
Self-Organization
• Use morphogenesis, especially chemotaxis, as a
paradigm.
• Control parameters for the self-sorting behavior of
lower-level primitives.
• Design local interaction rules for general shape primitives.
• Analyze and direct the spatial self-organizing shape
formation process.
11. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Thesis
Two Self-Organizing Systems
• Robust self-sorting of a mixture of heterotypic agents.
• Morphogenetic primitives for self-organizing shape
formation.
Robust Self-Organizing Shape Formation
• Synthesize macroscopic parameters that effectively
describe the shape evolution process.
• Use the identified macroscopic parameters to direct the
shape formation process.
12. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Contributions
A methodology of programming self-organizing primitives to
consistently form user-defined global shapes.
Self-sorting of heterotypic agents
Paradigms for designing biology-based algorithms of
self-organization.
Morphogenetic primitives
An ‘organic’ way of modeling predefined macroscopic shapes with
self-organizing primitives.
Investigation of statistical moments
Accurate prediction of the final outcome and insights into the
relationship between macroscopic features and aggregated outcome.
Directing self-organizing shape formation
Can be applied in multi-agent shape formation, swarm robotics and
sensor networks.
14. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Introduction
Cell Sorting in Biology
• The motions in chemotaxis may lead to cell-cell
aggregation, complex pattern formation or sorting of cells.
• The enclosure of one type of cell grouping by another.
• A fundamental phenomenon in morphogenesis,
embryogenesis, tumerogenesis and tissue development.
15. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Introduction
Cell Sorting Simulation
• The goal is to robustly produce a desired sorted structure.
• A mechanism that strictly quantifies how good a sorted
structure is.
• To perform empirical analysis on system parameters.
• To identify parameter ranges that always produce a
desired sorted structure.
16. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Introduction
Problem Description
• Using chemotaxis as a paradigm, how can we change
associated parameter values so that a desired sorted
structure can always be produced?
17. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Approach Overview
Based on
differential chemotactic response, motility and adhesion
• Two types of agents (T1 shaded blue and T2 shaded red)
are randomly placed in a 2D toroidal environment.
• Agents emit different chemicals into the environment and
respond to the chemical gradients sensed on the surfaces.
• Given proper predefined actions and parameters, sorted
structures can be created.
18. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Summary
• T1 blue cells emit chemical C1 to attract other T1 cells.
• As T1 cells begin to attach to each other, they emit a
second chemical C2 to attract T2 red cells.
• Probabilistic attachment and detachment enable a
symmetric result.
19. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Results
Self-organizing heterotypic agents sorted into a layered structure.
20. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Evaluation Function of the Final Structure
R
blue
avg =
1
n
X
pixelblue
i
2T1
Dist(pixel
blue
i , Center),
R
red
avg =
1
m
X
pixelred
i
2T2
Dist(pixel
red
i , Center),
blue
=
v
u
u
u
t
1
n
X
pixelblue
i
2T1
(Rblue
i
Rblue
avg )2,
red
=
v
u
u
u
t
1
m
X
pixelred
i
2T2
(Rred
i
Rred
avg )2,
fitness = 100/(
blue
+
red
).
The centroid of blue pixels is denoted as Center and R⇤
i is the distance between pixel i and Center.
21. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Parameter Ranges of Desired Sorted Structure
• A desired sorted structure has a fitness value above 1.40.
• 1 - Magnitude of chemotactic response to chemical 1.
• 2 - Magnitude of chemotactic response to chemical 2.
• PR - Probability of responding to a chemoattractant.
• PDetach - Probability of detachment.
• TS - Time between first attachment and T1’s production of C2.
• PAttach - Probability of attachment.
Type i PR PDetach PAttach TS
T1 3 0.4 – 0.7 0.1 - 9
T2 > 0.0 0.75 0.1 R-R: < 1.0 -
22. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Conclusion
Summary
• A self-sorting system that robustly produce a layered
two-cell-type structure.
• The structure is achieved by changing parameters of a
fixed cell level interaction.
Ultimate Goal
• To construct a general, robust self-organizing system for
different macroscopic structures.
24. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Introduction
Motivation
• Inspired by the biological phenomenon morphogenesis,
where shapes and structures emerge from low level
interactions.
• Cells emit and respond to chemicals in the environment.
• Cell movements produce large-scale aggregation.
• To design Morphogenetic Primitives (MP) for
self-organizing shape formation.
25. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Introduction
Problem Description
• Given predefined shape and initially disorganized
primitives, how to discover local interactions between the
primitives that direct them to aggregate into the
macroscopic target shape?
26. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
MP Design Principles
• Autonomous ‘agents’: there’s no ‘master designer’ that
directs the actions/motions of the MPs.
• Actions are based on local information: each MP emits a
finite field that can be sensed only by other primitives
within a certain range.
• MPs respond to information with identical prescribed
behaviors based on information received from the
environment.
• MPs have no representation of the final, macroscopic
shape to be produced.
• The shape emerges from the aggregation of local
interactions and behaviors, rather than from following a
plan to produce the shape.
27. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
MP Actions
• Emits artificial chemical into the environment.
• Senses cumulative chemical field around it.
• Calculates gradient and magnitude of movement (gradient
step).
• Probabilistically takes a gradient step.
• If there is a collision?
No – Takes step.
Yes – Take a tentative random step.
If still a collision, no movement.
28. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
General Approach
• Develop MP aggregation model, based on a previous
chemotaxis-driven cell aggregation model.
• Define chemical field around individual cells with arbitrary
mathematical functions
-Instead of the physical 1/r function.
• Discover local interaction rules (chemical field function)
that cause cells to form into specific shape by following
cumulative field.
• Genetic Programming is used to evolve chemical field
functions.
29. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Framework
Terminate?
End
(d+Log(cos(theta)))
((exp((theta-theta))-sin(Log(theta)))+
(Divide(Log((0.142492)),(d*d))*
Divide(((-0.805624)-t),Divide(theta,t))))
((Log(d)-((0.166099)*theta))+
Divide(t,(0.798272)))
0.208388
0.165218
0.161841
0.516388(d-sin((d+(0.377292))))
Open
Beagle
( GP
framework )
Shape
Primitive
Aggregation
Simulator
Fitness
Evaluation
Target Shape (2D image)
MP Aggregate (2D image)
Fitness Value
Field Funcions
30. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Gear Field Function Visualization
MP chemical field Cumulative chemical field
31. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
MPs Form into A Gear Shape
(Loading gearmovie.mp4)
33. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Conclusion
Summary
• We have successfully used genetic programming to evolve
local field functions for a number of simple user-defined
shapes.
• We have shown that chemotaxis can be used as a
paradigm for interactions among the primitives.
• Self-Organizing MPs do not always aggregate into the
desired form.
• The ellipse shape has 100% repeatability, diamond 99%,
hourglass only 10%, the letter ‘S’ 99% and the letter ‘b’ 9%
and triangle 7%.
34. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Conclusion
Ultimate Goal
• To construct a robust self-organizing system for different
macroscopic structures.
36. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Bifurcation in the Shape Formation System
Due to Randomness and Sensitivity to Initial Conditions
• Every simulation begins with a different uniform random
initial configuration.
• Primitives stochastically follow the gradient of the
cumulative field.
37. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Predicting the Final Outcome
If a feature can predict an outcome, it may also be able to
control it.
Specific Steps
1. Identify macroscopic features that capture shape evolution.
2. Generate feature vectors for a number of bifurcating
shapes.
3. Classification algorithm to predict bifurcating outcomes.
4. Leave-one-out cross validation for model evaluation.
38. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Statistical Moments
Mean, Variance, Skewness and Kurtosis
M1 =
1
n
nX
i=1
Xi, (1)
M2 =
1
n
nX
i=1
(Xi µ)2
, where µ =
1
n
nX
i=1
Xi, (2)
M3 = [
1
n
nX
i=1
(Xi µ)3
]/(M2)3/2
, (3)
M4 = [
1
n
nX
i=1
(Xi µ)4
]/(M2)2
. (4)
for all Xi, where (i = 1, 2, ...n) and Xi =< xi, yi >.
39. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Feature Vector
• Our shape simulation evolves over time, at each simulation
time t, we obtain four moments associate with the time
Mi(t), where i = 1, 2, 3, 4.
• Consider an interval of 5⌧, that is, Mi(t 2⌧), Mi(t ⌧),
Mi(t), Mi(t + ⌧) and Mi(t + 2⌧), we fit a straight line to
these five points, and we obtain the slope of the line ki.
• Feature vector is:
[Mx1
(t), My1
(t), Mx2
(t), My2
(t),
Mx3
(t), My3
(t), Mx4
(t), My4
(t)
kx1
(t), ky1
(t), kx2
(t), ky2
(t),
kx3
(t), ky3
(t), kx4
(t), ky4
(t)] (5)
40. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Using Support Vector Machines
• We consider predicting bifurcating outcomes a
classification problem.
• We use the LIBSVM library with the RBF kernel and use
grid search to find optimal SVM parameters, i.e., C and .
• The size of the training set is 200, with 100 in each
category.
63. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Dataset Information and Bifurcation Prediction
64. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Dataset Information and Bifurcation Prediction
65. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Dataset Information and Bifurcation Prediction
66. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Dataset Information and Bifurcation Prediction
67. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Conclusion
• Statistical moments capture the dynamic macroscopic
structure of MP swarm.
• We are able to predict the outcome of the shape formation
evolution at 10% of the simulation time steps with an
accuracy of 81% to 91%.
• The next step is to control or influence the shape evolution
so that the primitives consistently form into one stable
configuration.
69. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Goal
Motivation
• A mixed self-sorting system of two types of agents - only
one kind of structure.
• A chemotaxis-based self-organizing shape formation
system - not robust.
Directing Spatial Self-Organization
• To develop a robust shape formation system based on
self-organizing primitives.
• To analyze the shape formation process and identify
macroscopic features to control the self-organizing
process.
70. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Overview
• Previously identified statistical moments as significant
macroscopic features.
• Analyze the dynamics of the MP swarm’s statistical
moments during the aggregation process.
• Use statistical moments as thresholds to generate biased
initial conditions that lead the aggregation into a desired
shape.
71. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Analysis of Statistical Moments Over Time
Step
77. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Analysis of Statistical Moments Over Time
78. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Generating Constrained Biased Distributions
Steps
• Identify significant moment msig by plotting moment over
the entire simulation.
• Calculate non-overlapping value regions and specify
threshold value.
• Generate probability density functions for initial x and y
coordinates.
• Unconstrained coordinates initialized with uniform random
distribution.
• Sample from the probability density functions and accept
distributions whose significant moment msig meets the
threshold.
79. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Biased Initial Conditions and Results
(a) (b) (c) (d)
(top row) Biased initial conditions ((a) x skewness = -0.268, (b) y
kurtosis = 2.150, (c) x variance = 9,596, (d) x kurtosis = 1.88) that
robustly evolve (bottom row) into (a) a right-facing quarter-moon, (b) a
single ellipse, (c) three discs and (d) two line segments.
80. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Shape Evolution with Unbiased and Biased Initial
Conditions
81. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Shape Evolution with Unbiased and Biased Initial
Conditions
82. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Shape Evolution with Unbiased and Biased Initial
Conditions
83. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Shape Evolution with Unbiased and Biased Initial
Conditions
84. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Conclusion
• We have developed an agent-based self-organizing shape
formation system.
• We identify significant, distinguishing moment features for
each shape.
• Based on these moment features, we generate biased,
random initial conditions.
• By starting the shape formation process from biased
conditions, we are able to direct the final outcome. (75% to
100%)
86. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Summary
• Robust self-sorting of a mixture of heterotypic agents.
• Morphogenetic primitives for self-organizing shape
formation.
• Identified macroscopic features that effectively describe
the shape evolution process and accurately predict the
final outcome.
• Used the macroscopic features to direct the shape
formation process.
87. Introduction Self-Sorting Primitives Shape Primitives Predicting Self-Organization Directing Self-Organization Conclusion
Contributions
A methodology of programming self-organizing primitives to
consistently form user-defined global shapes.
Self-sorting of heterotypic agents
Paradigms for designing biology-based algorithms of
self-organization.
Morphogenetic primitives
An ‘organic’ way of modeling predefined macroscopic shapes with
self-organizing primitives.
Investigation of statistical moments
Accurate prediction of the final outcome and insights into the
relationship between macroscopic features and final aggregated
outcome.
Directing self-organizing shape formation
Can be applied in multi-agent shape formation, swarm robotics and
sensor networks.
