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Documents authored by Padalkin, Andreas

Document
DOI: 10.4230/LIPIcs.SAND.2024.18
Reconfiguration and Locomotion with Joint Movements in the Amoebot Model

Authors: Andreas Padalkin, Manish Kumar, and Christian Scheideler

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
We are considering the geometric amoebot model where a set of n amoebots is placed on the triangular grid. An amoebot is able to send information to its neighbors, and to move via expansions and contractions. Since amoebots and information can only travel node by node, most problems have a natural lower bound of Ω(D) where D denotes the diameter of the structure. Inspired by the nervous and muscular system, Feldmann et al. have proposed the reconfigurable circuit extension and the joint movement extension of the amoebot model with the goal of breaking this lower bound. In the joint movement extension, the way amoebots move is altered. Amoebots become able to push and pull other amoebots. Feldmann et al. demonstrated the power of joint movements by transforming a line of amoebots into a rhombus within O(log n) rounds. However, they left the details of the extension open. The goal of this paper is therefore to formalize the joint movement extension. In order to provide a proof of concept for the extension, we consider two fundamental problems of modular robot systems: reconfiguration and locomotion. We approach these problems by defining meta-modules of rhombical and hexagonal shapes, respectively. The meta-modules are capable of movement primitives like sliding, rotating, and tunneling. This allows us to simulate reconfiguration algorithms of various modular robot systems. Finally, we construct three amoebot structures capable of locomotion by rolling, crawling, and walking, respectively.
Cite as

Andreas Padalkin, Manish Kumar, and Christian Scheideler. Reconfiguration and Locomotion with Joint Movements in the Amoebot Model. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{padalkin_et_al:LIPIcs.SAND.2024.18,
  author =	{Padalkin, Andreas and Kumar, Manish and Scheideler, Christian},
  title =	{{Reconfiguration and Locomotion with Joint Movements in the Amoebot Model}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.18},
  URN =		{urn:nbn:de:0030-drops-198963},
  doi =		{10.4230/LIPIcs.SAND.2024.18},
  annote =	{Keywords: programmable matter, modular robot system, reconfiguration, locomotion}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2024.26
Brief Announcement: Collision Detection for Modular Robots - It Is Easy to Cause Collisions and Hard to Avoid Them

Authors: Siddharth Gupta, Marc van Kreveld, Othon Michail, and Andreas Padalkin

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
We consider geometric collision-detection problems for modular reconfigurable robots. Assuming the nodes (modules) are connected squares on a grid, we investigate the complexity of deciding whether collisions may occur, or can be avoided, if a set of expansion and contraction operations is executed. We study both discrete- and continuous-time models, and allow operations to be coupled into a single parallel group. Our algorithms to decide if a collision may occur run in O(n²log² n) time, O(n²) time, or O(nlog² n) time, depending on the presence and type of coupled operations, in a continuous-time model for a modular robot with n nodes. To decide if collisions can be avoided, we show that a very restricted version is already NP-complete in the discrete-time model, while the same problem is polynomial in the continuous-time model. A less restricted version is NP-hard in the continuous-time model.
Cite as

Siddharth Gupta, Marc van Kreveld, Othon Michail, and Andreas Padalkin. Brief Announcement: Collision Detection for Modular Robots - It Is Easy to Cause Collisions and Hard to Avoid Them. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 26:1-26:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gupta_et_al:LIPIcs.SAND.2024.26,
  author =	{Gupta, Siddharth and van Kreveld, Marc and Michail, Othon and Padalkin, Andreas},
  title =	{{Brief Announcement: Collision Detection for Modular Robots - It Is Easy to Cause Collisions and Hard to Avoid Them}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{26:1--26:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.26},
  URN =		{urn:nbn:de:0030-drops-199044},
  doi =		{10.4230/LIPIcs.SAND.2024.26},
  annote =	{Keywords: Modular robots, Collision detection, Computational Geometry, Complexity}
}
Document
DOI: 10.4230/LIPIcs.DNA.28.8
The Structural Power of Reconfigurable Circuits in the Amoebot Model

Authors: Andreas Padalkin, Christian Scheideler, and Daniel Warner

Published in: LIPIcs, Volume 238, 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (2022)

Abstract
The amoebot model [Derakhshandeh et al., SPAA 2014] has been proposed as a model for programmable matter consisting of tiny, robotic elements called amoebots. We consider the reconfigurable circuit extension [Feldmann et al., JCB 2022] of the geometric (variant of the) amoebot model that allows the amoebot structure to interconnect amoebots by so-called circuits. A circuit permits the instantaneous transmission of signals between the connected amoebots. In this paper, we examine the structural power of the reconfigurable circuits. We start with some fundamental problems like the stripe computation problem where, given any connected amoebot structure S, an amoebot u in S, and some axis X, all amoebots belonging to axis X through u have to be identified. Second, we consider the global maximum problem, which identifies an amoebot at the highest possible position with respect to some direction in some given amoebot (sub)structure. A solution to this problem can then be used to solve the skeleton problem, where a (not necessarily simple) cycle of amoebots has to be found in the given amoebot structure which contains all boundary amoebots. A canonical solution to that problem can then be used to come up with a canonical path, which provides a unique characterization of the shape of the given amoebot structure. Constructing canonical paths for different directions will then allow the amoebots to set up a spanning tree and to check symmetry properties of the given amoebot structure. The problems are important for a number of applications like rapid shape transformation, energy dissemination, and structural monitoring. Interestingly, the reconfigurable circuit extension allows polylogarithmic-time solutions to all of these problems.
Cite as

Andreas Padalkin, Christian Scheideler, and Daniel Warner. The Structural Power of Reconfigurable Circuits in the Amoebot Model. In 28th International Conference on DNA Computing and Molecular Programming (DNA 28). Leibniz International Proceedings in Informatics (LIPIcs), Volume 238, pp. 8:1-8:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{padalkin_et_al:LIPIcs.DNA.28.8,
  author =	{Padalkin, Andreas and Scheideler, Christian and Warner, Daniel},
  title =	{{The Structural Power of Reconfigurable Circuits in the Amoebot Model}},
  booktitle =	{28th International Conference on DNA Computing and Molecular Programming (DNA 28)},
  pages =	{8:1--8:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-253-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{238},
  editor =	{Ouldridge, Thomas E. and Wickham, Shelley F. J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.28.8},
  URN =		{urn:nbn:de:0030-drops-167935},
  doi =		{10.4230/LIPIcs.DNA.28.8},
  annote =	{Keywords: progammable matter, amoebot model, reconfigurable circuits, spanning tree, symmetry detection}
}
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