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Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots Amira Abdel-Rahman, Aaron T. Becker, Daniel E. Biediger, Kenneth C. Cheung, Sndor P. Fekete, Benjamin Jenett, Eike Niehs , Christian Scheffer, Arne Schmidt,

  1. Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots Amira Abdel-Rahman, Aaron T. Becker, Daniel E. Biediger, Kenneth C. Cheung, Sándor P. Fekete, Benjamin Jenett, Eike Niehs , Christian Scheffer, Arne Schmidt, and Mike Yannuzzi

  2. Motivation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 1

  3. Robots-on-Tiles Model 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 2

  4. Copying Rotating TM-Transformation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 3

  5. Why should we care about connectivity? 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 4

  6. Why should we care about connectivity? 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 4

  7. Why should we care about connectivity? 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 4

  8. 1. Constructing a Bounding Box Given : A polyomino P. Wanted : A rectangular box that surrounds P. Constraint : The union of all tiles and all robots has to be connected at any time. P 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 5

  9. Constructing a Bounding Box • Two robots (one as a special marker) • 3 phases: 1. Finding a start position 2. Construction ▪ Clockwise ▪ Shifting ▪ Conflict on starting edge ▪ Hit a bounding box tile 3. Clean-Up (Finishing) 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 6

  10. 2. Scaling Polyominoes Given : A polyomino P, a constant c. P Wanted : Scale every tile of P by the constant factor c. c = 3 Constraint : The union of all tiles and all robots has to be connected at any time. 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 7

  11. Scaling Polyominoes • Pre-Step: Bounding box Idea: • For every node within the bounded area: • Place a 𝑑 × 𝑑 square • Marker for empty nodes of P 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 8

  12. Scaling Polyominoes 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  13. Scaling Polyominoes 1. Preparation Progress Connectivity Next to scale 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  14. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  15. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  16. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  17. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  18. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  19. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  20. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  21. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  22. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  23. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  24. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  25. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  26. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  27. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  28. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  29. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  30. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  31. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  32. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  33. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  34. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  35. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  36. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  37. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  38. Scaling Polyominoes → 2. Scaling 1. Preparation 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  39. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  40. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  41. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  42. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  43. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  44. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  45. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  46. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  47. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

  48. Scaling Polyominoes → → 3. Clean-Up 1. Preparation 2. Scaling 18/03/2020 | Eike Niehs | Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots | Slide 9

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