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Dissertation/Thesis Abstract

Minimizing the Maximum Distance Traveled to Form Patterns with Systems of Mobile Robots
by Coleman, Jared Ray, M.Sc.C.S., California State University, Long Beach, 2020, 59; 27834173
Abstract (Summary)

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). In this thesis, we begin to develop a theoretical understanding of the min-max traversal pattern formation problem. We show the necessary conditions every valid solution must satisfy and present a solution for systems of three robots. Our work also led to an interesting 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.

Indexing (document details)
Advisor: Morales Ponce, Oscar
Commitee: Ebert, Todd, Lam, Shui
School: California State University, Long Beach
Department: Computer Engineering and Computer Science
School Location: United States -- California
Source: MAI 82/3(E), Masters Abstracts International
Subjects: Computer science, Robotics, Mathematics
Keywords: Distributed, Formation, Geometry, Pattern, Robotics
Publication Number: 27834173
ISBN: 9798664789737
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