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Theory of Distributed Systems
Models and Algorithms for Programmable Matter
Christian Scheideler
Joint work with
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Theory of Distributed Systems
Models and Algorithms for Programmable Matter Christian Scheideler - - PowerPoint PPT Presentation
Models and Algorithms for Programmable Matter Christian Scheideler - - PowerPoint PPT Presentation
Theory of Distributed Systems Models and Algorithms for Programmable Matter Christian Scheideler Joint work with Theory of Distributed Systems Motivation Scene with T1000 from Terminator 2 Movie: Primitives? Algorithms? 2 Theory of
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Theory of Distributed Systems
Motivation
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Theory of Distributed Systems
Motivation – Programmable Matter Today
Kilobots M-blocks Prismatic cubes
Modular and swarm robotics:
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Theory of Distributed Systems
Motivation - Applications
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Theory of Distributed Systems
Basic Problems
Shape formation: Coating problems:
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Theory of Distributed Systems
Towards a model for programmable matter
Our basic approach:
- Programmable matter consists of simple, intelligent particles that
can move, bond, and exchange information through bonds
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Theory of Distributed Systems
Towards a model for programmable matter
At all times, particles have to form connected structure
- Which structure to form?
- How to move along a given structure?
- Can a particle drag other particles with it?
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Theory of Distributed Systems
Towards a model for programmable matter
Candidates for the structure formed by the particles: … or even irregular structures
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Theory of Distributed Systems
Towards a model for programmable matter
Problem with latter two grids: Some particles cannot move along edges without losing connectivity … but maybe it would also be fine to do diagonal movements
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Theory of Distributed Systems
Towards a model for programmable matter
But how can two diagonally moving particles pass each other? … so it seems best to use triangular grid
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Theory of Distributed Systems
Towards a model for programmable matter
How to move while maintaining a rigid structure for the other particles?
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Theory of Distributed Systems
Towards a model for programmable matter
How to move while maintaining a rigid structure for the other particles? Also, how to handle conflicting movements?
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Theory of Distributed Systems
Towards a model for programmable matter
Solution: use extensions and contractions
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Theory of Distributed Systems
Towards a model for programmable matter
Solution: use extensions and contractions In case of a conflict, go back to the previous position → allows us to handle concurrency!
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Theory of Distributed Systems
Towards a model for programmable matter
Other assumptions:
- Particles have limited (constant) memory and initially do not have
any global information about the system
- Particles have common chirality, but no global orientation
- Particles are activated in an asynchronous fashion
- Particles can only communicate via bonds
Name of our model: Amoebot model
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Theory of Distributed Systems
Towards a model for programmable matter
We do not consider:
- Energy
- Fault-tolerance
- Gravity (just 2D)
Name of our model: Amoebot model
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Relationship with other models Existing models insufficient for programmable matter.
- Cellular automata
- Static cell-based view, not agent-based view
- DNA self-assembly, population protocols, …
- No controlled movements
- Swarm robotics
- No connectivity, powerful sensing
- Nubot model (Woods, Chen, Goodfriend, Dabby, Winfree, Yin 2013)
- Particle can drag others with it
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Problems considered here
- Leader Election
- Shape Formation
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Why Leader Election?
It is easy to show: Line formation solvable ⇒ Leader election solvable Hence, Leader election not solvable ⇒ Line formation not solvable ⇒ Ability to elect leader crucial for suitability of prog. matter model Is geometric information (regular structure, chirality) needed? Itai & Rodeh [FOCS’81]: leader election cannot be solved in our model without geometric information (since it is impossible on the cycle). Hence, also line formation is not solvable without geometric information.
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Theory of Distributed Systems
Leader Election - The Big Picture
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Theory of Distributed Systems
Leader Election – Subphase 1
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Theory of Distributed Systems
Leader Election – Subphase 1
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Theory of Distributed Systems
Leader Election – Subphase 2
1
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Theory of Distributed Systems
Leader Election – Subphase 3
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Leader Election – The details
For the local protocol lots of issues have to be resolved. The main challenges are: 1. Segment length comparison 2. Candidacy transferal 3. Solitude verification 4. Inner/Outer Boundary Test Solutions rely heavily on token passing schemes and the regularity of the grid graph.
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Leader Election – Solitude verification
y x
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Leader Election – Inner/Outer Boundary Test ∑ = +360° ≙ +6 ∑ = −360° ≙ −6 = 4 𝑛𝑛𝑛 5 = 1 𝑛𝑛𝑛 5
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Leader Election With the ability of LE a lot of problems get easier:
- Shape Formation
- Majority
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The Takeaway Slide
- The Amoebot model is a simple and reasonable model to study
programmable matter.
- There is an interesting connection between having geometric
information and solving leader election.
- Leader election and shape formation are intrinsically related.
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