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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
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Volume:
3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Algorithmic Foundations of Dynamic Networks (SAND) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-05-31
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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.
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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
https://doi.org/10.4230/LIPIcs.SAND.2024.26
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.
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
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References
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