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Efficiently Reconfiguring a Connected Swarm of Labeled Robots

Authors Sándor P. Fekete , Peter Kramer , Christian Rieck , Christian Scheffer , Arne Schmidt

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Author Details

Sándor P. Fekete
  • Department of Computer Science, TU Braunschweig, Germany
Peter Kramer
  • Department of Computer Science, TU Braunschweig, Germany
Christian Rieck
  • Department of Computer Science, TU Braunschweig, Germany
Christian Scheffer
  • Faculty of Electrical Engineering and Computer Science, Bochum University of Applied Sciences, Germany
Arne Schmidt
  • Department of Computer Science, TU Braunschweig, Germany

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Sándor P. Fekete, Peter Kramer, Christian Rieck, Christian Scheffer, and Arne Schmidt. Efficiently Reconfiguring a Connected Swarm of Labeled Robots. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ISAAC.2022.17

Abstract

When considering motion planning for a swarm of n labeled robots, we need to rearrange a given start configuration into a desired target configuration via a sequence of parallel, continuous, collision-free robot motions. The objective is to reach the new configuration in a minimum amount of time; an important constraint is to keep the swarm connected at all times. Problems of this type have been considered before, with recent notable results achieving constant stretch for not necessarily connected reconfiguration: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of d, the total duration of an overall schedule can be bounded to 𝒪(d), which is optimal up to constant factors. However, constant stretch could only be achieved if disconnected reconfiguration is allowed, or for scaled configurations (which arise by increasing all dimensions of a given object by the same multiplicative factor) of unlabeled robots. We resolve these major open problems by (1) establishing a lower bound of Ω(√n) for connected, labeled reconfiguration and, most importantly, by (2) proving that for scaled arrangements, constant stretch for connected reconfiguration can be achieved. In addition, we show that (3) it is NP-hard to decide whether a makespan of 2 can be achieved, while it is possible to check in polynomial time whether a makespan of 1 can be achieved.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Computing methodologies → Motion path planning
Keywords
  • Motion planning
  • parallel motion
  • bounded stretch
  • makespan
  • connectivity
  • swarm robotics

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