Recognition and Reconfiguration of Lattice-Based Cellular Structures - - PowerPoint PPT Presentation

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Recognition and Reconfiguration of Lattice-Based Cellular Structures - - PowerPoint PPT Presentation

Oct 11, 2022 449 likes •998 views

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,

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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, Sándor P. Fekete, Benjamin Jenett, Eike Niehs, Christian Scheffer, Arne Schmidt, and Mike Yannuzzi

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

Motivation

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

Robots-on-Tiles Model

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

Copying Rotating TM-Transformation

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

Why should we care about connectivity?

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

Why should we care about connectivity?

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

Why should we care about connectivity?

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

  • 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

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

  • 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)

Constructing a Bounding Box

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

  • 2. Scaling Polyominoes

Given: A polyomino P, a constant c. Wanted: Scale every tile of P by the constant factor c. Constraint: The union of all tiles and all robots has to be connected at any time.

c = 3 P

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

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

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

Scaling Polyominoes

  • 1. Preparation

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

Scaling Polyominoes

  • 1. Preparation

Progress Connectivity Next to scale

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

9

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

Scaling Polyominoes

  • 1. Preparation

→

  • 2. Scaling

→

  • 3. Clean-Up

C = 3

9

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

Adapting Algorithms

  • Given any Robots-on-Tiles algorithm – A
  • We construct an algorithm A’ that ensures

connectivity:

  • 1. Scale P by a factor c
  • 2. c steps in A’ for every step in A
  • 3. Fill rows/columns with c × 𝑑 segments, when

it is first entered.

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C = 3

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

Summary

Bounding Box Scaling c = 3 Adapting algorithms to fulfill connectivity constraints

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

Proof of Concept

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