@inproceedings{007393dbcd4a4872b40a236d3b1b6c44,
title = "Brief Announcement: Collision Detection for Modular Robots – It Is Easy to Cause Collisions and Hard to Avoid Them",
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(n2 log2 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.",
keywords = "Collision detection, Complexity, Computational Geometry, Modular robots",
author = "Siddharth Gupta and \{van Kreveld\}, Marc and Othon Michail and Andreas Padalkin",
note = "Publisher Copyright: {\textcopyright} Siddharth Gupta, Marc van Kreveld, Othon Michail, and Andreas Padalkin.; 3rd Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2024 ; Conference date: 05-06-2024 Through 07-06-2024",
year = "2024",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SAND.2024.26",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Arnaud Casteigts and Fabian Kuhn",
booktitle = "3rd Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2024",
address = "Germany",
}