Document Open Access Logo

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 , Andreas Padalkin

PDF

File

Thumbnail PDF
PDF
LIPIcs.SAND.2024.26.pdf
  • Filesize: 0.6 MB
  • 5 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Modular robots
  • Collision detection
  • Computational Geometry
  • Complexity

Metrics

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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.SAND.2024.26

Author Details

Siddharth Gupta
  • BITS Pilani, Goa Campus, India
Marc van Kreveld
  • Utrecht University, The Netherlands
Othon Michail
  • University of Liverpool, United Kingdom
Andreas Padalkin
  • Paderborn University, Germany

Funding

  • Padalkin, Andreas: This author was supported by the DFG Project SCHE 1592/10-1.

Acknowledgements

The authors thank all participants of the Bertinoro Workshop on Distributed Geometric Algorithms, in particular Peyman Afshani for suggesting the O(nlog² n) time solution for detecting collisions when there are no couplings. We thank Irina Kostitsyna and Christian Scheideler for the organization, and the latter also for proposing the collision detection problem. Finally, we thank Jesper Nederlof for some useful observations.

References

  1. Nada Almalki and Othon Michail. On geometric shape construction via growth operations. Theor. Comput. Sci., 984:114324, 2024. Google Scholar
  2. Greg Aloupis, Sébastien Collette, Erik D. Demaine, Stefan Langerman, Vera Sacristán Adinolfi, and Stefanie Wuhrer. Reconfiguration of cube-style modular robots using O(log n) parallel moves. In ISAAC, volume 5369 of Lecture Notes in Computer Science, pages 342-353. Springer, 2008. Google Scholar
  3. Joshua J. Daymude, Andréa W. Richa, and Christian Scheideler. The canonical amoebot model: algorithms and concurrency control. Distributed Comput., 36(2):159-192, 2023. Google Scholar
  4. Zahra Derakhshandeh, Shlomi Dolev, Robert Gmyr, Andréa W. Richa, Christian Scheideler, and Thim Strothmann. Brief announcement: amoebot - a new model for programmable matter. In SPAA, pages 220-222. ACM, 2014. Google Scholar
  5. Michael Feldmann, Andreas Padalkin, Christian Scheideler, and Shlomi Dolev. Coordinating amoebots via reconfigurable circuits. J. Comput. Biol., 29(4):317-343, 2022. Google Scholar
  6. Siddharth Gupta, Marc J. van Kreveld, Othon Michail, and Andreas Padalkin. Collision detection for modular robots - it is easy to cause collisions and hard to avoid them. CoRR, abs/2305.01015, 2023. Google Scholar
  7. George B. Mertzios, Othon Michail, George Skretas, Paul G. Spirakis, and Michail Theofilatos. The complexity of growing a graph. In ALGOSENSORS, volume 13707 of Lecture Notes in Computer Science, pages 123-137. Springer, 2022. Google Scholar
  8. Damien Woods, Ho-Lin Chen, Scott Goodfriend, Nadine Dabby, Erik Winfree, and Peng Yin. Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In ITCS, pages 353-354. ACM, 2013. Google Scholar
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact