Genetic and developmental computing architectures: Modular robotics, Lecture 3

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Genetic and developmental computing
architecturesModular robotics, Lecture 3
Auke J. Ijspeert Biologically Inspired Robotics
Group (BIRG) Swiss Federal Institute of
Technology, Lausanne
30 January 2006
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Content of lecture 3 control of reconfiguration

• Overview of challenges
• Metrics
• Centralized planning approach
• Decentralized approaches
• Growing rules
• Cellular automata

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Challenges

• Reconfiguration a sequence of moves,
  attachment, and detachments for changing a
  structure A into a structure B
• Note the previous lecture only covered sequences
  of moves for locomotion (not attachments and
  detachments)

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Challenges

• Finding the right and shortest sequences of
  moves, attachments and detachments is very hard
  because
• The number of options to explore is usually huge
  (grows exponentially), and systematic exploration
  is not feasible
• The moves must be valid, e.g. avoid inter-module
  collisions, avoid splitting the system in
  different parts, respect torque-limit
  constraints,
• Therefore heuristics are needed for searching
  good solutions
• Ideally, the approach should be decentralized and
  use a limited amount of computation and
  intermodule communication

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Challenges

• In todays lecture we will review four articles
  that address these challenges
• A theoretical paper on metrics
• A paper presenting a centralized planning
  approach
• And two papers presenting decentralized
  approaches

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Content of lecture 3 control of reconfiguration

• Overview of challenges
• Metrics
• Centralized planning approach
• Decentralized approaches
• Growing rules
• Cellular automata

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Metrics

• Metrics are very important for quantatively
  measuring how different one configuration is from
  the other
• Interesting article Useful Metrics for Modular
  Robot Motion Planning, Pamecha et al, IEEE
  Transactions on Robotics and Automation, VOL. 13,
  NO. 4, 1997, pp 531-545

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Metrics

• Metrics for two-dimensional systems

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Metrics

• Possible application creating arbitrary
  structures, e.g. for encapsulating dangerous
  materials

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Metrics
Metrics for two-dimensional configurations a
quantitative measure of the difference between
two configurations
Difference?
Note the paper assumes that the total number of
modules n is a constant
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Metrics
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The discrete metric

• Trivial example the discrete metric
• The distance between two configurations is zero
  if the two configurations are identical,
  otherwise it is one.
• Example

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The overlap metric

• Another example the overlap metric
• The distance between two configurations is the
  number of modules that do not overlap between the
  two configurations (n is the number of modules).
• Example

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The overlap metric

• In other words, the overlap metric tells you the
  number of modules that need to be moved to go
  from one configuration to the other.
• The overlap metric is useful but it does not tell
  how many moves need to be made to change one
  configuration into the other.

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The minimal-number-of-moves metric

• Another example the minimal-number-of-moves
  metric
• Where Mmin is the fewest moves needed to go from
  A to B
• Example

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The minimal-number-of-moves metric

• The minimal-number-of-moves metric is a very
  useful metric since it is directly provides the
  information needed to make optimal
  reconfigurations
• Unfortunately it has no representation other than
  explicitly solving a computationally explosive
  problem and recording the sum of moves which is
  minimal.
• This is not practical in most applications

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The optimal assignment metric

• Another example the optimal assignment metric
• Where f is the cost function of an assignment
  between A and B

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The optimal assignment metric

• Example of different assignments
• Intuitively the second assignment is better

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The optimal assignment metric

• An assignment is determined by the variable mij,
  which is 1 if the module ai is assigned to module
  bj, and 0 otherwise.
• It is given a cost dij which is the lattice
  distance between module ai and bj.
• Hence the cost function for a given assignment
• The optimal assignment metric is the minimal cost
  of all possible assignments

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The optimal assignment metric

• The optimal assignment metric can be computed
  with several algorithms, e.g. the Hungarian
  algorithm
• The computational cost is far less than for the
  minimal-number-of-moves metric

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Combining metrics

• Interestingly, metrics can be combined and still
  form metrics.
• Indeed
• A possible interesting metric combines the
  overlap metric and the optimal assignment metric,
  the combined metric

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Testing metrics

• The authors tested these different metrics using
  a simulated annealing (SA) algorithm
• A SA is a stochastic algorithm that finds a
  (local) minimum of a function (here a metric)
• It uses a process similar to a heated metal that
  is slowly cooled down into a specific shape
• It is used by the authors to evaluate which of
  the metrics performs best with three different
  problems

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Problem 1

• Results
• Overlap metric performs poorly
• Optimal-assignment metric and combined metric
  perform (equally) well

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Problem 2

• Results
• Overlap metric performs poorly
• Optimal-assignment metric and combined metric
  perform (equally) well

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Problem 3
base
obstacle

• Results
• Overlap metric performs very poorly
• Optimal-assignment metric performs OK
• Combined metric performs best

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Metrics summary

• Defining metrics is very important for
  quantatively measuring how different one
  configuration is from the other
• There are multiple different metrics available,
  but they are not all good for finding the
  shortest number of moves for the reconfiguration
• On the particular problems tested, the optimal
  assignement metric and the combined metric
  systematically produce better results than the
  optimal overlap metric.

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Content of lecture 3 control of reconfiguration

• Overview of challenges
• Metrics
• Centralized planning approach
• Decentralized approaches
• Growing rules
• Cellular automata

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Planning-based approach
Article A self-reconfigurable modular robot
reconfiguration planning and experiments, E.
Yoshida et al, The International Journal of
Robotics Research, 2002. The article presents a
method for continuously reconfiguring a group of
MTRAN modules in order to do locomotion It is a
centralized planning-based approach
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Planning

• The method is designed for the MTRAN II modules
• Each module has two servo motors with aligned
  axis
• The modules can attach to each other on a regular
  orthogonal grid of size a.
• Constraint each module has one active part and
  one passive part, and only passive-action
  connection are feasible

a
movie
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Planning

• The planner will use three types of atomic
  motion
• pivot motion,
• forward-roll motion and
• mode conversion.

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Atomic motion Pivot motion
Note it is assumed that the environment, i.e.
the grid, has active and passive connectors
Attached to grid
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Atomic motion Forward-role motion
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Atomic motion Mode conversion
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Planning

• The goal of the planning algorithm is to enable
  of group of modules to trace a 3D trajectory in
  the lattice grid.
• The desired 3D trajectory is provided.
• Example

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Planning

• The planning algorithm simplifies the
  problem by doing the planning
  for 4-module blocks
• A block is useful because it is the smallest
  group of modules that has an isotropic shape that
  can be connected at any of its faces.
• This isotropic geometry enables one to easily
  configure various sizes of 3D structures and to
  maintain the connectivity of all the modules in a
  cluster composed of these blocks.
• This block also has the advantage that it is
  simple to plan a global motion along a 3D
  trajectory.

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Planning

• In addition to blocks, the planning algorithms
  will use converters a couple of modules that
  have different rotation axis directions
• The converter modules are used to change the
  direction of the rotation axis of the modules in
  the chain cluster.

2 converter modules
3 blocks
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Planning

• Goal of the planning algorithm
• Given the block-based trajectory of locomotion as
  the input, the motion of each module must be
  planned.
• Difficulties
• The modules non-isotropic geometrical
  properties make it difficult to obtain the motion
  sequence in a straightforward manner.
• 3D motion usually requires a combined
  cooperative motion sequence with other
  surrounding modules.
• The cooperative motion sequence must be
  carefully chosen in each individual local
  configuration to avoid collisions between modules
  or loss of connectivity during the motion.

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Planning

• The authors propose a two-layered motion planner
  consisting of
• the global flow planner and
• the local motion scheme selector.
• The global flow planner searches possible module
  paths and motion orders to provide the global
  cluster movement, called flow, according to the
  desired trajectory.
• The local motion scheme selector verifies that
  the paths generated by the global planner are
  valid for each member module of the block
  according to the possible motion orders, by
  repeatedly applying rules from the database.

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Planning
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Example
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Global flow planner

• The global flow planner is designed for serial
  clusters composed of four-module cubic blocks.
• It computes the motion of a block such that the
  tail block is transferred toward the given
  heading direction.
• The motion of a block is done by sending
  individual modules towards destination positions
  (mainly with forward-role motions).
• For each module, the global flow planner will
  produce different possible paths towards
  different possible target positions
• The motion scheme selector will decide which one
  is chosen

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Example of different possible paths
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Motion scheme selector

• The motion scheme selector
• Checks that paths proposed by the global flow
  planner are feasible (e.g. checks that all
  modules remain connected, and that collisions are
  avoided)
• It generates all the moves and cooperative moves
  necessary (e.g. movement of other modules to
  rotate the moving module) using a database of
  possible local reconfigurations
• The database has 30 hand-coded if-then rules
• It computes which of the possible paths require
  the lowest number of moves

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Planning

• Example of a rule for the local reconfiguration

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Results example
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Results example
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Results example
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Planning summary
An approach using planning algorithms for
reconfiguration The approach is centralized,
i.e. there is a master doing all the computation
and telling modules what to do. Two-layered
approach one global flow planner for blocks, one
planner for local moves (the motion scheme
selector) The method allows continuous
reconfiguration for locomotion Can be adapted for
other reconfiguration tasks by modifying the
global flow planner
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Content of lecture 3 control of reconfiguration

• Overview of challenges
• Metrics
• Centralized planning approach
• Decentralized approaches
• Growing rules
• Cellular automata

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Growing rules

• Creating modular robotic structures with growing
  rules
• Emergent Structures in Modular Self-reconfigurable
  Robots, H. Bojinov, A. Casal, T. Hogg,
  Proceedings of the 2000 IEEE International
  Conference on Robotics Automation (ICRA2000)
• Motivation
• it is sometimes difficult to know in advance the
  desired final structure of the modular robotic
  system.
• E.g. it can be difficult because the environment
  is complex and stochastic
• It is sometimes easier to determine desirable
  properties.

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Growing rules

• The paper uses Proteo modules in the shape of a
  rhombic dodecahedron, a three dimensional shape
  (polyhedron) with 12 identical sides in the shape
  of a rhombus.
• The simulated proteo module moves by rotating
  around edges
• The shape is useful to make dense structures
  movie

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Growing rules

• Idea
• Determine a set of growing rules which lead to
  desirable properties, not a specific structure
• Concepts used in the approach
• Growth the process that influences the motion of
  modules and the creation of structures
• Seeds modules that attract other modules in
  order to grow structures
• Scents signals that are transmitted between
  modules.
• Modes the mode of a module is its present
  finite-state machine state. Possible modes
  include sleep, seed, search, node, and final.

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Growing rules

• Transmission of scents
• scent signals are transmitted between modules.
• Each module keeps a number in its memory
  representing the strength of the scent at its
  location.
• At each time step, modules look at their
  neighbors and update this number to be the
  minimum value plus one.
• Scent values are therefore an approximation of
  the distance to a scent-emitting module.
• Experiments typically use one or two different
  scents

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Example Growing Chains

• All modules are initially in SLEEP mode except
  one that is randomly set to SEED.
• Control rules for each module
• If in SLEEP mode, if a scent is detected, go to
  SEARCH mode.
• If in SEARCH mode, propagate scent and move along
  scent gradient.
• If in SEED mode, emit scent, and if a module has
  appeared in the direction of growth, set that
  module to SEED mode, and go to FINAL mode.
• If in FINAL mode, propagate scent.

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Example growing chains
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Example Growing Recursive Branching

• All modules are initially in SLEEP mode except
  one that is randomly set to NODE.
• Control rules for each module
• If in SLEEP mode, if regular scent is detected,
  go to SEARCH mode.
• If in SEARCH mode, propagate both scents and move
  along the regular scent gradient.
• If in SEED mode, propagate the node scent, and
  emit a regular scent if there is a neighboring
  module in the direction of growth of the branch,
  set that module to be a seed, and go to FINAL
  mode.
• If in FINAL mode, propagate both scents if the
  node scent is weak (high value), go to NODE mode.
• If in NODE mode, emit both scents, spawn seeds in
  random directions, until a certain count is
  reached, then go to INODE mode.
• If in INODE mode, emit a node scent and propagate
  the regular scent.

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Example Growing Recursive Branching
These type of structures are useful to create
limbed robots, or hands, etc. Note humans show
only two levels of branching (limbsfingers), but
sometimes having more could be useful
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Growing rules

• Other examples lattice behavior

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Growing rules

• Other examples Sponge structures

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Growing rules

• Grasping an object

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Growing rules grasping an object

• Initially all modules are in SLEEP mode, except
  for eight modules that are set to SEED mode (to
  create eight branches to grow toward the object).
  
• Two types of seeds are used SEED modules, and
  TOUCHSEED modules.
• Initially growth is caused by SEED modules, but
  once the object is reached, seeds transfer to the
  TOUCHSEED state. The two types of seeds allow
  modules in SEARCH mode to know whether to grow in
  the direction of the object (to reach it) or to
  grow the structure around the object (to grasp
  it).
• The modules are assumed to know the approximate
  direction to the object and to have contact
  sensors to detect when the object has been
  reached.

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Growing rules

• Note the system grasps the object despite the
  fact that has no knowledge of the exact direction
  of the object, how far it is, or what shape and
  size it has.

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Growing rules

• Dynamically adapting to external forces
• Scents for growing legs (and switches to disband
  mode) are generated depending on load sensors.
• The system can adapt to slowly varying weight
  shifts

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Growing rules summary

• Use of local rules to grow structures
• No global planning, it is a decentralized method
• Rules are designed for generating desirable
  properties
• Desired configuration is not explicitly defined
• Stochastic process
• Requires insights for designing the local rules,
  no well defined methodology
• An optimization algorithm (e.g. a GA) could be
  used for designing the rules
• Constraint all modules need to remain connected
  all the time
• Since only local information is used, there is a
  risk of getting stuck in suboptimal structures

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Content of lecture 3 control of reconfiguration

• Overview of challenges
• Metrics
• Centralized planning approach
• Decentralized approaches
• Growing rules
• Cellular automata

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Reconfiguration with Cellular automatas

• Controlling Self-reconfiguration using Cellular
  Automata and Gradients, K. Stoy, proceedings of
  IAS8, 2004
• Two-step process
• Generate a CA representation from a CAD model of
  the desired configuration
• Do the self-reconfiguration process using local
  interactions and local communication about
  gradient information

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Reconfiguration with CAs example
Light gray Wandering mode
Dark gray Final mode
Black Seed mode
Movie
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Cellular automata

• The basic module has the shape of a cube
• It can connect to neighbors on any facet
• It can sense for each facet if the is a neighbor
  or not
• It can communicate with neighbors (exchange
  information about states and gradients)
• It is capable of sliding along the facets of
  other cubes
• The whole system is assumed to be in a
  gravity-free environment or to have one fixed
  element (the first seed)

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Cellular automata

• Example of motion

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Cellular automata

• Example of motion

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Cellular automata

• Example of motion

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Cellular automata

• Transforming a CAD model of the desired
  configuration into a cellular automata
• Use a special scaffold structure that can fill
  the desired shape without dead-ends
• Note that this creates only an approximation of
  the structure (e.g. it has many holes)

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Cellular automata

• Transforming a CAD model of the desired
  configuration into a cellular automata
• The structure is approximated with a complete set
  of modules
• Modules are removed such that an approximate
  structure can be constructed with a chain of
  scaffolds
• Each module i is assigned a unique number s(i)
• For each neighboring pair of modules i, j a rule
  is generated. This rule is of the form if the CA
  of the module in direction i to j is in state
  s(j) then this CA should change to state s(i).

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Cellular automata

• Example
• Each module has the complete CA rule table
• Modules can be in different modes wandering,
  seed, and final
• All modules start in the wandering mode, except
  one which is in the seed mode.

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Cellular automata

• The self-reconfiguration algorithm has three
  components
• a state propagation mechanism,
• a mechanism to create gradients in the system,
  and
• a mechanism for moving the modules.

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Cellular automata

• The state propagation mechanism
• Initial random configuration
• One arbitrary module becomes a seed is given a
  state number randomly chosen from the set s(i)
• Neighbor modules change their state according to
  the CA rules
• If neighbor modules are missing, the seed module
  attracts a wandering module with a gradient
  signal
• This module will act as a new seed.
• A module stops acting as a seed when all the
  neighbor relationships, described by the cellular
  automaton rules, are satisfied. It is then in
  final mode.

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Cellular automata

• Creating a gradient using local information
• A seed module sends out a constant integer (the
  concentration of an artificial chemical) to all
  its neighbors.
• A receiving module calculates the concentration
  of the artificial chemical at its position by
  taking the maximum received value and subtracting
  one.
• This value (as well as the direction towards
  climbing the gradient) is then propagated to all
  neighbors and so on.
• When the concentration reaches zero the gradient
  is not further propagated.
• This means that the source can decide the range
  of the gradient.

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Cellular automata

• Mechanisms for moving the modules
• Wandering modules climb the vector gradient to
  reach unfilled positions.
• Thanks to the scaffold desired structure, there
  are no local optima (i.e. no dead-ends)
• Note, the wandering modules cannot move
  independently of each other, because they depend
  on each other for connection to the robot. There
  is a risk of splitting the system in different
  parts.
• The problem can be avoided by following these
  rules

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Results

• This algorithm was tested with different initial
  and final configurations
• It converged systematically to the final
  configurations
• The number of moves to reach the final
  configuration is reasonable
• Not significantly more than the theoretical
  minimum

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Results
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Results
Movie of a complex example
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Cellular automata summary

• This approach allows the generation of specific
  desired structures, with only local interactions
  and local communication. It is a decentralized
  approach.
• The system converges because of how the CA is
  encoded (no possible dead-ends), and the number
  of moves is reasonable
• The CA rule table can be quite large (up to
  62N), i.e. modules should have enough memory
• The system is meant to generate one particular
  structure, not to switch from one to another

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End of this lecture