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Reconfiguration and Locomotion with Joint Movements in the Amoebot Model

Authors Andreas Padalkin , Manish Kumar , Christian Scheideler

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Andreas Padalkin
  • Paderborn University, Germany
Manish Kumar
  • Bar-Ilan University, Israel
Christian Scheideler
  • Paderborn University, Germany

Funding

This work has been supported by the DFG Project SCHE 1592/10-1 and the Israel Science Foundation under Grants 867/19 and 554/23.

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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)
https://doi.org/10.4230/LIPIcs.SAND.2024.18

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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Cooperation and coordination
  • Theory of computation → Computational geometry
Keywords
  • programmable matter
  • modular robot system
  • reconfiguration
  • locomotion

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