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 BDA 2016 – July 25, 2016

Theory of Distributed Systems Inspiration 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. BDA 2016 2

Theory of Distributed Systems Motivation - Applications BDA 2016 3

Theory of Distributed Systems The amoebot Model Overarching Constraint: Maintain Connectivity BDA 2016 4

Theory of Distributed Systems The amoebot Model “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 BDA 2016 5

Theory of Distributed Systems Shape Formation Problem BDA 2016 6

Theory of Distributed Systems Naive Shape Formation Problem Video on this slide was deleted to decrease file size. For naïve Shape Formation algorithms (Hexagon & Triangle) visit http://sops.cs.upb.de/ . BDA 2016 7

Theory of Distributed Systems Universal Shape Formation Problem In general not possible, i.e., BDA 2016 8

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) BDA 2016 9

Theory of Distributed Systems Universal Shape Formation Problem BDA 2016 10

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. BDA 2016 11

Theory of Distributed Systems Universal Shape Formation Problem Note: 𝑃 𝑜 rounds is not possible if we start in an arbitrary initial configuration. Solution: BDA 2016 12

Theory of Distributed Systems Universal Shape Formation Algorithm Movement Primitives: 2) Triangle expansion/ contraction/ rotation ( 𝑃 ℓ rounds) expansion contraction ℓ rotation BDA 2016 13

Theory of Distributed Systems Universal Shape Formation Algorithm Intermediate Structure BDA 2016 14

Theory of Distributed Systems Universal Shape Formation Algorithm Intermediate Structure BDA 2016 15

Theory of Distributed Systems Universal Shape Formation Algorithm Building the final shape: 13 15 10 6 12 14 4 16 3 11 2 9 7 1 5 8 BDA 2016 16

Theory of Distributed Systems 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 . BDA 2016 17

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 BDA 2016 18

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 BDA 2016 19

Theory of Distributed Systems 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/ BDA 2016 20