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UBC Theses and Dissertations

A qualitative representation for manipulator kinematics and other vector and scalar fields Dangelmaier, Heidi Therese


Over the last several years a branch of Artificial Intelligence called Qualitative Reasoning has received much attention. A qualitative reasoner use qualitative values such as increasing, boiling and turbulent to analyze the behavior of physical systems. Existing qualitative frameworks have focused on physical systems whose qualitative values can be identified given the value of a single parameter. This precludes the application of qualitative models to physical systems whose properties require the values of several parameters. An example of such a system is the kinematics of a robotic manipulator. With this motivation, this thesis answers the following: What is a Qualitative model? Although current approaches appear diverse, they share a common mathematical foundation. This foundation is used to reformulate the qualitative model as a set of equivalence relations. The other question answered is: What extensions are needed to handle multivariate properties such as those encountered in the manipulator paradigm? The equivalence classes associated with qualitative models are geometrically shown to be connected hyperspaces. We show that existing frameworks are limited in the types of hyperspaces they can represent. The major ideas in this thesis are illustrated using manipulator kinematics.

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