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.
|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|
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