Minimizing The Maximum Distance Traveled To Form Patterns With Systems of Mobile Robots

Jared Coleman, Evangelos Kranakis, Oscar Morales Ponce, Jaroslav Opatrny, Jorge Urrutia, Birgit Vogtenhuber

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


In the pattern formation problem, robots in a system must self-coordinate to form a given pattern, regardless of translation, rotation, uniform-scaling, and/or reflection. In other words, a valid final configuration of the system is a formation that is similar to the desired pattern. While there has been no shortage of research in the pattern formation problem under a variety of assumptions, models, and contexts, we consider the additional constraint that the maximum distance traveled among all robots in the system is minimum. Existing work in pattern formation and closely related problems are typically application-specific or not concerned with optimality (but rather feasibility). We show the necessary conditions any optimal solution must satisfy and present a solution for systems of three robots. Our work also led to a surprising result that has applications beyond pattern formation. Namely, a metric for comparing two triangles where a distance of 0 indicates the triangles are similar, and 1 indicates they are fully dissimilar.
Original languageEnglish
Title of host publicationProceedings of the 32nd Canadian Conference on Computational Geometry (CCCG 2020)
Place of PublicationSaskatoon, Saskatchewan, Canada
Number of pages7
Publication statusPublished - 2020
Event32nd Canadian Conference on Computational Geometry: CCCG 2020 - Virtuell, Canada
Duration: 5 Aug 20207 Aug 2020


Conference32nd Canadian Conference on Computational Geometry
Abbreviated titleCCCG 2020


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