Universal Shape Formation for Programmable Matter (Thim Strothmann) - - PowerPoint PPT Presentation

Theory of Distributed Systems

Universal Shape Formation for Programmable Matter

(Thim Strothmann)

Joint work with

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Theory of Distributed Systems

Inspiration

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Video on this slide was deleted to decrease file size. For inspiration Video (scene from Big Hero six) visit https://www.youtube.com/watch?v=fF1rDKEC0TI.

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Motivation - Applications

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The amoebot Model

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Overarching Constraint: Maintain Connectivity

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The amoebot Model

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• “Standard” asynchronous computation model
• Only one particle is activated in each time step
• Once activated a particle can compute, communicate and perform one

move

• an adversary activates particles
• Round: every particle is activated at least once

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Shape Formation Problem

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Naive Shape Formation Problem

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Video on this slide was deleted to decrease file size. For naïve Shape Formation algorithms (Hexagon & Triangle) visit http://sops.cs.upb.de/ .

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Universal Shape Formation Problem

In general not possible, i.e.,

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Theory of Distributed Systems

Universal Shape Formation Problem

Input: constant size set of faces Goal:

• build shape given by faces (scaled-up and possibly rotated)
• scale to include all particles

(no leftover particles)

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Universal Shape Formation Problem

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Theory of Distributed Systems

Universal Shape Formation Problem

Our Result: Given any shape described by a constant number of faces, our algorithm builds that shape using all particles in the system in 𝑃 𝑜 rounds.

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Universal Shape Formation Problem

Note: 𝑃 𝑜 rounds is not possible if we start in an arbitrary initial configuration. Solution:

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Universal Shape Formation Algorithm

Movement Primitives: 2) Triangle expansion/ contraction/ rotation (𝑃 ℓ rounds)

expansion contraction rotation

ℓ

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Universal Shape Formation Algorithm

Intermediate Structure

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Theory of Distributed Systems

Universal Shape Formation Algorithm

Intermediate Structure

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Theory of Distributed Systems

Universal Shape Formation Algorithm

Building the final shape:

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1 5 4 3 2 6 7 9 8 12 11 10 16 15 14 13

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Universal Shape Formation Algorithm

The devil is in the details:

• Take care of the imperfection of the intermediate structure without

moving it.

• Make up for the estimation errors of ℓ.

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Theory of Distributed Systems

Universal Shape Formation Algorithm

The devil is in the details:

• Triangles have to be cut to different sizes (+ incorporate waste).
• The intermediate structure might block the final building process

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Theory of Distributed Systems

Summary & Future Work

Result: Given any shape described by a constant number of faces, our algorithm builds that shape using all particles in the system in 𝑃 𝑜 rounds. Interesting Challenges:

• arbitrary configuration of low diameter
• non-constant size shapes
• 3D
• Failures

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References

Corresponding Publication:

Zahra Derakhshandeh, Robert Gmyr, Andréa W. Richa, Christian Scheideler, Thim Strothmann: Universal Shape Formation for Programmable Matter. SPAA 2016: 289-299 (http://doi.acm.org/10.1145/2935764.2935784)

For videos of some of our algorithms and a (slightly outdated) publication history in the topic visit:

http://sops.cs.upb.de/

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